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LOS  ANGELES 


MicUl  LowtfaJU 


KAUFMANN'S 

Pathology 

A  very  necessary  work  for 
the  medical  library.  Thor- 
ough in  details;  beautiful 
illustrations;  the  latest 
German  edition  translated 
into  English  and  aug- 
mented by  recent  ad- 
vances and  special  facts 
pertaining  to  American 
medicine.  Dr.  Reimann, 
Director  of  Lankenau  Re- 
search Institute,  Phila- 
delphia, is  translator  and 
editor  of  English  edition. 
He  has  added  over  100 
drawings. 

1072  Illustrations 
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Medical  Association. 

P.  BLAKISTON'S  SON  &  CO.,  Inc. 

1012  Walnut  St.        Philadelphia 


(OVER) 


PRISMS 

THEIR  USE  AND  EQUIVALENTS 


BY 

JAMES  THOR1NGTON,  A.  M.,  M.  D. 

AUTHOR  OF  "REFRACTION  AND  HOW  TO  REFRACT";  "THE  OPHTHALMOSCOPE  AND  HOW 
TO  USE  IT";  "RETINOSCOPY".    PROFESSOR  OF  DISEASES  OP  THE  EYE  IN  THE 
PHILADELPHIA  POLYCLINIC  AND  COLLEGE  FOR  GRADUATES  IN  MEDI- 
CINE; FELLOW  OF  THE  COLLEGE  OF  PHYSICIANS  OF  PHILADEL- 
PHIA; MEMBER  OP  THE  AMERICAN  OPHTHALMOLOGICAL 
SOCIETY;  OPHTHALMIC  SURGEON  TO  THE  PRES- 
BYTERIAN HOSPITAL,  ETC 


118  ILLUSTRATIONS 
OF  WHICH  18  ARE  COLORED 


PHILADELPHIA 

P.   BLAKISTON'S   SON   &   CO 

1012  WALNUT  STREET 
1913 


COPYRIGHT,  1913,  BY  P.  BLAKISTON'S  SON    &  Co. 


THE. MAPLE' PRESS- YOBK. PA 


35V 


PREFACE 


The  preparation  of  this  book  on  "Prisms,  their  use  and 
equivalents,"  has  been  prompted  by  the  request  of  many 
students  and  correspondents,  though  it  is  written  pri- 
marily for  those  who  may  desire  a  more  extended 
knowledge  on  this  branch  of  refraction  than  is  con- 
tained in  works  on  Ophthalmology. 

In  fact,  this  volume  is  in  part  a  compilation  of  the 
writer's  lectures  on  prisms  delivered  during  the  winter 
course  at  the  Philadelphia  Polyclinic. 

The  author's  double  prism,  a  new  and  delicate 
test,  for  the  detection  of  errors  of  muscular  imbalance 
whether  of  small  or  great  amount,  is  incorporated  in  the 
text. 

To  make  the  subject-matter  more  entertaining,  the 
writer  has  not  limited  himself  to  the  consideration  of 
prisms  in  ophthalmic  practice  alone,  and  by  omitting 
mathematic  formulas  and  inserting  many  illustrations, 
the  text  is  made  easy  of  comprehension. 


CONTENTS 


CHAPTER  I. 

PAGE 

GENERAL  DESCRIPTION      i 

CHAPTER  II. 
REFRACTION  OF  LIGHT  AND  REFRACTION  OF  LIGHT  BY  PRISMS   .    .     10 

CHAPTER  III. 

OPTICAL  EFFECT  OF  A  PRISM 23 

CHAPTER  IV. 
PRISM  NOMENCLATURE;  DENNETT'S  METHOD;  PRENTICE'S  METHOD; 

AND  NEUTRALIZING  PRISMS      40 

CHAPTER  V. 

COMBINED  PRISMS 54 

CHAPTER  VI. 

COMBINING    A    PRISM    WITH    A    SPHERE,    CYLINDER    OR    SPHERO- 
CYLINDER      61 

CHAPTER  VII. 

USES  OF  PRISMS  IN  OPHTHALMOLOGY 78 

CHAPTER  VIII. 

PRISM  TREATMENT  FOR  HETEROPHORIA  AND  HETEROTROPIA    .    .    .113 

CHAPTER  IX. 

GENERAL  REMARKS   ON  PRISMS   AND  THE  PRISMATIC  EFFECT  OF 
LENSES ' 134 

INDEX 141 


vn 


PRISMS 


CHAPTER  I 
GENERAL  DESCRIPTION 

A  Prism  is  a  wedge-shaped  portion  of  a  refracting 
medium  (usually  of  glass)  contained  between  two  plane 
polished  surfaces  (Figs,  i,  2,  3  and  5),  or  a  prism  is  a 
transparent  homogeneous  medium  with  two  plane  sur- 
faces which  are  not  parallel  to  each  other.  Prisms 
used  in  the  practice  of  ophthalmology  are  seldom  very 


FIG    i.— Prism  on  base.     PX  =  Edge  or  Apex.     BASE  =  Base.    PBAX 
and  PESX  =  Faces  or  Surfaces.     BPE  and  AXS  =  Angle. 

strong  and  therefore  have  their  surfaces  placed  at  a 
very  acute  angle. 

The  sides  of  a  prism  are  the  inclined  surfaces,  also 
spoken  of  as  refracting  surfaces  or  faces  (PBAX  and 
PE  SX  in  Figs,  i,  2  and  3). 


PRISMS 


The  edge  (also  frequently  spoken  of  as  the  apex  of  a 
prism)  is  that  part  of  the  prism  where  the  two  plane  sur- 
faces meet  (P  X  in  Figs,  i,  2  and  3). 


FIG.  2.— Prism  on  edge.    PX  =  Edge  or  Apex.     BASE  =  Base.     PBAX 
and  PESX  =  Faces  or  Surfaces.     BPE  and  AXS  =  Angle. 


FIG.  3.— Prism  on  side.    PX   =  Edge  or  Apex.     BASE   =  Base.     PBAX 
and  PESX  =  Faces  or  Surfaces.     BPE  and  AXS  =  Angle. 

The  base  of  a  prism  is  the  thick  part  of  the  prism 
and  is  opposite  to  the  edge  or  apex  (BASE  in  Figs,  i, 
2  and  3).  The  base  of  the  prism  is  occasionally  referred 
to  as  the  third  surface. 


GENERAL   DESCRIPTION 


The  refracting  angle  is  a  physical  feature  of  the 
prism  and  is  the  angle  at  which  the  two  sides  or  refract- 
ing surfaces  come  together;  it  is  this  angle  together  with 
the  index  of  refraction  of  the  glass  (or  medium)  which 


Base 
FIG.  4.— Principal  section  of  a  prism. 


determines  the  strength  of  the  prism  (B  P  E  and  A  X  S 
in  Figs,  i,  2  and  3). 

Section  of  a  Prism. — Dividing  or  cutting  through  a 
prism  at  right  angles  to  its  refracting  surfaces  or  faces 


B  A 

FIG.  5. — Rectangular  prism. 


makes  a  principal  section;  this  is  shown  in  Fig.  4,  and 

will  assist  in  explaining  what  has  just  been  described. 

Shape  or  Form  of  a  Prism. — By  this  is  meant  the 

outline  or  contour  of  the  prism  and  not  the  section,  this 


PRISMS 


FIG.  6.  — Dr. 
Noyes'  prism  bar 
or  battery. 


latter  being  wedge-shaped  (Fig.  4). 
Figs,  i,  2  and  3  illustrate  square 
prisms.  Fig.  5,  a  rectangular  prism 
and  Figs.  7,  8  and  9,  round  prisms. 
Rectangular  prisms  are  not  ordinarily 
used  in  ophthalmology.  Square 
prisms,  while  easily  handled  cannot 
be  placed  in  the  ordinary  trial-frame. 

The  late  Dr.  Noyes  recommended 
a  battery  of  prisms  which  was  a  series 
of  small  square  prisms  of  increasing 
strength,  numbered  in  degrees,  1/2, 
i,  2,  3,  4,  and  6,  mounted  in  a  frame 
as  shown  in  Fig.  6.  The  operator  or 
patient  held  this  vertically  in  front 
of  the  eye  and  moved  it  up  or  down 
when  it  was  desired  to  get  a  stronger 
or  weaker  prism  before  the  eye.  Two 
of  these  batteries  or  "bars"  were  re- 
quired, one  with  the  bases  of  the 
prisms  placed  laterally  and  the  other 
with  the  bases  placed  vertically. 
These  batteries  of  prisms  are  not  now 
in  general  use. 

Round  or  Circular  Prisms  (Figs. 
7,  8  and  9). — These  are  found  in  the 
trial  case  and  as  their  diameters  (set 
in  cells)  are  the  same  as  the  spheres 
and  cylinders  they  fit  easily  into  the 
trial-frame.  Unfortunately  the  base 
of  the  prism  being  quite  thick  in 


GENERAL   DESCRIPTION  5 

some  instances  (Fig.  10)  takes  up  considerable  space 
in  the  trial-frame  and  therefore  when  in  the  frame  it  has 
to  be  placed  in  the  outer  opening,  so  as  to  leave  room 
for  the  sphere  and  cylinder  back  of  it.  If  placed  in 
the  back  opening  of  the  frame  it  is  liable  to  rub  against 
the  eye  lashes  or  the  eye  lid. 

Recognition  of  the  Edge  or  Apex  and  Base  of  the 
Prism. — When  a  prism  is  square  (Fig.  i)  in  contour  its 
long  edge  or  apex  is  immediately  and  easily  detected 


^.^  i " 

FIG.  7. — Spuare  prism  marked  foe  cutting  out  the  round  or  circular  prism. 


and  likewise  its  base  (Fig.  7),  but  when  round  or  circular 
(Figs.  8  and  9)  in  contour,  its  thinnest  part  will  then  be 
recognized  as  a  point  in  the  apex  or  edge  of  the 
original  square  prism  (Fig.  7).  The  thickest  part  or 
base  of  the  round  or  circular  prism  is  diametrically 
opposite  to  the  edge  or  apex  and  it  too  corresponds  to  a 
point  or  line  in  the  base  of  the  original  square  prism 
(Fig.  7).  These  two  points  indicating  the  edge  (or 
apex)  and  base  of  a  round  or  circular  prism  are  marked 
with  a  broad  diamond  scratch  on  the  glass  (Fig.  8)  the 
same  as  seen  on  cylinder  lenses,  to  indicate  the  axis  of 
the  cylinder.  Likewise  the  number  of  the  prism  is  also 


6  PRISMS 

scratched  upon  the  glass.  The  position  of  the  base  of  a 
circular  prism  is  occasionally  marked  with  a  white  or 
black  line  connecting  the  two  plane  (circular)  surfaces  or 
faces  at  their  greatest  separated  points  (Fig.  7).  This 
method  of  marking  the  position  of  the  prism  edge,  base 
and  number,  does  not  meet  with  the  writer's  approval,  as 
they  are  not  sufficiently  distinct  and  he  therefore  has  the 
prisms  in  his  own  trial  case  marked  as  shown  in  Fig.  9. 
These  prisms  have  very  wide  black  metal  frames  without 


FIG.  8. — Prism  in  wire  frame.     Diamond  scratches  on  glass  to  indicate  base 
and  apex  line,  also  number  of  prism. 

handles,  the  wide  frame  or  cell  acting  as  a  handle.  The 
direction  of  the  edge  and  number  of  the  prism  are 
marked  in  white  on  this  black  metal  frame  as  shown  in 
the  figures  referred  to  and  the  base  is  indicated  by  an 
arrow  head,  also  marked  in  white. 

Base-apex  Line. — This  is  an  imaginary  straight 
line  connecting  the  edge  (apex)  with  the  center  of  the 
base  (A  B  in  Fig.  n).  This  base-apex  line  is  of  as 
great  importance  to  a  knowledge  and  use  of  prisms  as 
the  axis  line  of  a  cylinder  lens.  In  Chapter  II  it  will  be 
shown  that  an  object  viewed  through  a  prism  always 


GENERAL  DESCRIPTION  7 

appears  displaced  in  the  direction  of  the  edge  of  the 
prism  and  exactly  parallel  to  the  base-apex  line  (Fig.  31). 

The  Axis  of  a  Prism. — This  is  an  imaginary  straight 
line  midway  between  the  edge  and  the  base  and  at  right 
angles  to  the  base-apex  line,  therefore  parallel  to  the 
edge  (X  S  in  Fig.  n). 

The  Plane  of  a  Prism. — This  is  midway  between  the 
two  plane  surfaces,  bisecting  the  angle  of  the  prism 
(Fig.  n). 


FIG.  9. — Prism  with  wide  frame  showing  markings  of  base  and  apex  and 
number  on  frame  or  cell. 

Position  of  a  Prism. — When  a  prism  is  placed  in 
front  of  an  eye  its  position  is  indicated  or  described  by 
the  direction  of  the  base-apex  line  and  this  direction  of 
the  base  must  always  be  carefully  specified  in  the  pre- 
scription. Base  down  means  that  the  thickest  part  of 
the  prism  is  toward  the  cheek,  this  may  be  written  in  the 
prescription,  Base  down  axis  90°.  Base  up  means  that 
the  base-apex  line  is  still  vertical  but  the  base  is  directed 
upward  or  toward  the  brow  and  this  may  be  written  in 
the  prescription,  Base  up  axis  90°.  Base  in  means  that 
the  base-apex  line  is  horizontal  and  the  base  of  the 


8  PRISMS 

prism  toward  the  nose,  this  may  be  written  in  the  pre- 
scription, Base  in  axis  180°.  Base  out  means  that  the 
base-apex  line  is  horizontal  and  the  base  of  the  prism 
is  toward  the  temple,  this  may  be  written  in  the  pre- 
scription, Base  out  axis  180°. 

The  base  of  the  prism  may  be  placed  in  any  desired 
direction  or  meridian  but  the  prescriber  must  specify 
definitely  in  his  prescription — (i)  the  strength  of  the 
prism,  (2)  which  eye  the  prism  is  for,  and  (3)  whether 


FIG.  10. — Profile  view  of  Fig.  9. 

the  base  is  up,  down,  in  or  out;  or  up  and  in,  or  up  and 
out,  or  down  and  in,  or  down  and  out ;  for  instance,  the 
following : 

Right  Eye,  2  Prism,  base  down  axis  75°;  2  Prism  base 
up  axis  75°;  2  Prism  base  down  axis  45°  or  2  Prism  base 
down  and  out  axis  45°;  2  Prism  base  up  axis  135°  or  2 
Prism  base  up  and  out  axis  135°,  etc.  The  reader  may 
obtain  a  clearer  idea  on  this  point  by  referring  to  the 
arrow  marking  on  the  cell  of  the  prism  pictured  in  Fig.  9, 
and  if  he  will  place  a  prism  in  a  trial-frame  and  study  it 


GENERAL   DESCRIPTION  9 

in  the  positions  just  described  he  will  obtain  a  definite 
knowledge  of  the  position  of  prisms  before  the  eye. 

The  prisms  in  the  trial  case  are  made  of  crown  glass 
which  is  practically  isotropic  and  therefore  has  but 
little  dispersive  power,  whereas  prisms  made  of  flint 
glass  or  rock  crystal  are  not  found  in  the  trial  case  as 
such  prisms  are  highly  dispersive  (anisotropic)  and  are 
principally  used  for  the  production  of  the  spectrum 
(Fig.  43). 


B 

FIG.  ii. — BA  =  Base-apex  line.    XS  =  Axis. 

Achromatic  Prisms. — These  are  seldom  if  ever 
prescribed,  because  they  are  heavy,  cumbersome  and 
expensive.  Such  prisms  can  be  made  by  joining  or 
cementing  together  two  prisms  of  different  strength  and 
of  different  index  of  refraction,  one  of  flint  and  the  other 
of  crown  glass,  with  the  base  of  one  to  the  edge  of  the 
other. 


CHAPTER  II 


REFRACTION  OF  LIGHT  AND  REFRACTION  OF 
LIGHT  BY  PRISMS 

For  a  proper  understanding  of  the  action  of  prisms 
upon  light  it  is  necessary  to  briefly  review  some  facts  on 
the  subject  of  refraction  in  general. 

Refraction. — From  the  Latin  "refrangere,"  meaning 
to  bend  back,  i.e.,  to  deviate  from  a  straight  course. 


o 


FIG.  12. — Illustrating  refraction  through  a  piece  of  plate  glass  with  parallel 

surfaces. 

Refraction  may  therefore  be  denned  as  the  deviation 

which  takes  place  in  the  direction  of  rays  of  light  as  they 

pass  from  one  medium  into  another  of  different  density. 

Two  laws  govern  the  refraction  of  rays  of  light : 

i.  A  ray  of  light  passing  from  a  rare  into  a  dense 


10 


REFRACTION    OF    LIGHT  II 

medium   is   deviated   toward  the  perpendicular  (A  in 
Fig.  12). 

2.  A  ray  of  light  passing  from  a  dense  into  a  rare 
medium  is  deviated  from  the  perpendicular  (R  in  Fig. 
12).  Aside  from  these  laws,  there  are  other  facts  in  re- 
gard to  rays  of  light  which  should  have  consideration. 
A  ray  of  light  will  continue  its  straight  course  through 
any  one  or  any  number  of  different  transparent  media, 
no  matter  what  their  densities,  so  long  as  it  forms  right 
angles  with  the  surface  or  surfaces  (P  P  in  Fig.  13). 


^      Ice 

£ 

£     Flint  Glass 

^ 

L. 

Crown  Glass 

f 

^     Plate  Glass 

J 

i 

FIG.  13. — Illustrating  the  passage  of  a  perpendicular  ray  through  transparent 
media  of  different  density  with  parallel  surfaces. 

Such  a  ray  is  spoken  of  as  the  perpendicular  or  normal. 
Such  surfaces  are  plane,  the  surfaces  and  perpendicular 
forming  right  angles. 

In  the  study  of  refraction  the  incident  and  refracted 
ray  may  be  reversed,  that  is  to  say,  the  refracted  ray 
may  be  called  the  incident  ray,  and  the  incident  ray  may 
be  called  the  refracted  ray;  for  instance,  in  Fig.  12,  the 
incident  ray  A  becomes  the  refracted  ray  R;  now  if  R 
is  considered  the  incident  ray,  it  would  become  the 
refracted  ray  at  A. 


12  PRISMS 

Figure  12  shows  the  ray  P  P  perpendicular  to  a  piece 
of  plate  glass  with  plane  surfaces.  The  thick  ray  A  in 
air  is  incident  at  O  on  the  surface  S  F  and  is  bent  in  the 
glass  toward  the  perpendicular  (P  P),  fulfilling  the  first 
law  of  refraction.  The  dotted  line  indicates  the  original 
direction  of  the  incident  ray  A  and  the  direction  it  would 
have  pursued  if  it  had  not  been  refracted.  As  the  ray 
A  in  the  glass  comes  to  its  second  surface  at  R  it  under- 
goes the  second  law  of  refraction  and  passing  into  the 


FIG.  14. — Illustrating  the  critical  angle. 

rarer  medium  (air)  it  is  bent  from  the  perpendicular  (P 
P).  The  ray  now  continues  its  original  direction  paral- 
lel with  the  dotted  line,  but  it  has  been  deviated  from 
its  original  course,  it  has  undergone  lateral  displace- 
ment. Attention  must  be  directed  to  the  thickness  of 
the  incident  ray  A  as  it  falls  upon  the  surface  S  F,  as 
only  part  of  it  is  refracted,  and  part  of  it  is  reflected, 
the  reflected  portion  is  marked  D.  This  accounts  for 
the  thinness  of  the  ray  A  in  the  glass.  A  substance  that 
could  transmit  or  absorb  all  the  rays  of  light  coming  to 
it  (if  such  a  substance  existed)  would  be  invisible.  Re- 
flection therefore  always  accompanies  refraction.  Fi- 


REFRACTION   OF   LIGHT  13 

nally  if  the  refracted  ray  A'  in  Fig.  12  is,  for  illustration, 
considered  the  incident  ray  at  R,  it  would  be  deviated 
toward  P'  P'  in  the  glass  and  make  its  exit  at  O  and  be 
the  refracted  ray  at  A.  This  demonstrates  the  path  of 
the  incident  ray  to  become  the  refracted,  or  the  re- 
fracted to  become  the  incident  ray,  i.e.,  the  path  of 
the  ray  is  reversible. 

Critical  Angle.  Limiting  Angle  of  Refraction. — 
This  is  the  angle  of  incidence  which  just  permits  a  ray 
of  light  in  a  dense  medium  to  pass  into  a  rare  medium. 
The  size  of  the  critical  angle  depends  upon  the  index  of 
refraction  of  different  substances.  The  critical  angle 
for  crown  glass  is  40°  49'. 

Figure  14  shows  an  electric  light  suspended  in  water. 
The  ray  from  this  light  which  forms  an  angle  of  48°  35' 
with  the  surface  of  the  water  will  be  refracted  and  pass 
out  of  the  water,  grazing  its  surface;  but  those  rays 
which  form  an  angle  greater  than  48°  35'  will  not  pass 
out  of  the  water,  but  will  be  reflected  back  into  it.  The 
surface  separating  the  two  media  beyond  this  point  of 
48°  35'  becomes  a  reflecting  surface  and  acts  as  a  plane 
mirror. 

Index  of  Refraction. — By  this  is  meant  the  relative 
density  of  a  substance  (not  its  specific  gravity)  or  the 
comparative  length  of  time  required  for  a  ray  of  light 
to  travel  a  definite  distance  in  different  substances.  The 
absolute  index  of  refraction  is  the  density  of  any  substance 
as  compared  with  a  vacuum.  According  to  the  first  law 
of  refraction,  a  ray  of  light  passing  from  a  rare  into  a 
dense  substance  is  refracted  toward  the  perpendicular; 
in  other  words  the  angle  of  refraction  is  smaller  under 


PRISMS 


these  circumstances  than  the  angle  of  incidence.  In 
the  study  of  the  comparative  density  of  any  substance 
it  will  be  seen  that  the  angle  of  refraction  is  usually 
smaller  the  more  dense  the  substance;  this  is  well 
illustrated  in  Figs.  15  and  16.  The  greater  the  density, 
the  slower  the  velocity,  or  the  more  effort  apparently 


FIG.  15.  FIG.  16. 

FIG.  15. — Angle  of  deviation  in  glass. 

FIG.  16. — Angle  of  deviation  in  diamond. 

for  the  wave  or  ray  to  pass  through  the  substance.  A 
ray  passes  through  a  vacuum  without  resistance,  but 
in  its  course  through  air  it  is  slightly  impeded,  so  that 
air  has  an  index  of  refraction  compared  with  a  vacuum 
of  1.00029+,  but  this  is  so  very  slight  that  air  and  a 
vacuum  are  considered  as  one  for  all  purposes  in  ophthal- 


Vacuum 


AA/XAA/XA.  \AAAAAAA  /UUUWUUl  Ir 


Air 


Glass 


-''  Diamond 


FIG.  17. — Illustrating  the  comparative  density  of  different  substances. 

mology  (Fig.  17).  To  find  the  index  of  refraction  of  any 
substance  as  compared  with  a  vacuum  it  is  only  neces- 
sary to  divide  the  sine  of  the  angle  of  incidence  by  the 
sine  of  the  angle  of  refraction  and  the  quotient  will  be 
the  index.  In  Fig.  18  the  angle  of  incidence  I  C  P  is  the 
angle  formed  by  the  incident  ray  I  with  the  perpendicu- 


REFRACTION    OF    LIGHT 


lar  P  P.  Drawing  the  circle  P  H  P  O  around  the  point 
of  incidence  C  and  then  drawing  the  sines  X  D  and  F  B 
perpendiculars  to  the  perpendicular  P  P,  divide  the  sine 
X  D  of  the  angle  of  incidence  by  the  sine  F  B  of  the  angle 
of  refraction,  in  this  instance  water  compared  with  air, 
X  D  equalling  4  and  F  B  equalling  3,  then  4  divided  by 


FIG.  18.  —  Illustrating  the  comparative  index  of  refraction. 


3  equals  4/3  or  1.33+,  the  index  of  refraction  of  water 
compared  with  air.  To  find  the  index  of  refraction  of 
a  rare  compared  with  a  dense  substance,  divide  the  sine 
of  the  angle  of  refraction  by  the  sine  of  the  angle  of  inci- 
dence, i.e.,  air  as  compared  with  water,  would  be  3/4 
or  0.75. 

THE  REFRACTIVE  INDEXES  OF  SOME  ORDINARY  MEDIA 


Vacuum i 

Air i  .000,294 

Pure  water i .  3336 

Sea  water i  .343 

Alcohol i  .365 

Diamond 2  .487 


Canada  balsam i .  530 

Crown  glass i .  540 

Rock  salt i .  545 

Rock  crystal i .  548 

Flint  glass i  .635 


i6 


PRISMS 


Besides  a  knowledge  of  refraction  preliminary  to 
understanding  the  action  which  prisms  have  upon  light, 
the  reader  should  also  understand  or  know  what  is 
meant  by  the  following  terms  in  trigonometry. 


G 


F  ~          "  E 
FIG.  19.— AB,  BC,  CD,  DE,  EF,  FG,  GH  and  HA  =  Arcs  of  the  circle. 


FIG.  20.— SE  =  Sine  of  the  Arc  AC. 


Arc  and  Arc  of  an  Angle. — This  is  the  portion  of 
the  circumference  of  a  circle  included  between  two  radii 
(Fig.  19  and  A  C  in  Fig.  20). 


REFRACTION    OF   LIGHT  17 

Sine  of  an  Arc. — A  perpendicular  line  extending  from 
one  end  of  an  arc  to  the  diameter  drawn  through  the 
other  end  of  the  arc  (S  E  in  Fig.  20  is  the  sine  of  the 
arc  A  C). 

Tangent  (Latin  "tangere"— "to  touch").— The 
touching  or  meeting  of  a  curve  or  surface  at  a  point.  A 
tangent  is  a  straight  line  which  touches  the  circum- 
ference but  does  not  intersect  it  (Fig.  21). 


T 

FIG.  21.— TTTTT  =  Tangents. 

The  tangent  of  the  angle  is  a  line  drawn  perpen- 
dicularly from  the  extremity  of  one  radius  to  meet  the 
other  radius  prolonged  (T  S  in  Fig.  22).  A  reference  to 
Figs.  19,  20,  21  and  22  will  show  that  the  arc  is  less 
than  the  tangent  and  greater  than  the  sine,  in  fact  these 
quantities  are  always  controlled  by  the  magnitude  of  the 
angle. 


i8 


PRISMS 


Radian. — A  radian  is  an  angle  subtended  at  the 
center  of  any  circle  by  an  arc  equal  in  length  to  the 
radius  of  the  circle  (Fig.  23). 


C  T 


FIG.  22.— SAC  =  Acute  Angle.     SE  =  Sine.     SC  =  Arc.     TS  =  Tangent. 


FIG.  23. — Illustrating  the  radian. 

Prismatic  Action. — Rays  of  light  in  a  prism  con- 
tinue in  straight  lines  and  are  not  perceptibly  broken  up 
into  different  wave  lengths  (colors)  so  long  as  the  glass 
composing  the  prism  is  isotropic.  The  surfaces  of  a 


REFRACTION   OF    LIGHT  19 

prism  alone  deviate  the  rays  and  not  the  glass  between 
the  surfaces,  hence  the  reason  for  speaking  of  the  faces 
of  a  prism  as  refracting  surfaces.  Rays  of  light  which 
pass  through  a  prism  are  always  refracted  away  from 
the  edge  and  toward  the  base  of  the  prism. 

Maximum  Deviation  or  Refraction. — By  this  is 
meant  the  greatest  deviating  power  of  the  prism  and  it 
is  obtained  when  all  the  refraction  is  done  at  one  surface, 
namely,  (i)  if  an  incident  ray  is  perpendicular  to  the 


FIG.  24. — Illustrating  maximum  refraction  or  deviation.  FS  and  FX 
=  Surfaces.  AR  and  BP  =  Incident  Rays.  PD  and  RC  =  Refracted 
Rays. 

first  surface  of  a  prism,  then  it  will  pass  to  the  second 
surface  before  it  is  deviated  or  refracted  and  all  the 
refraction  in  this  instance  is  done  at  this  one  surface, 
namely,  as  the  ray  emerges  from  the  prism  (B  P,Fig.  24), 
(2)  or  if  the  entering  (incident)  ray  is  so  bent  or  re- 
fracted on  its  entrance  into  the  prism  (A  R  in  Fig.  24) 
that  it  becomes  a  perpendicular  (R  C)  at  the  second 
surface,  it  will  pass  out  of  this  second  surface  without 
any  further  deviation ;  all  the  refraction  taking  place  at 
the  first  surface. 


20  PRISMS 

Minimum  Deviation. — By  this  is  meant  the  least 
effect  or  the  smallest  amount  of  deviating  power  of  the 
prism;  this  takes  place  when  the  ray  in  the  prism  is 
parallel  with  the  base  in  an  equilateral  prism  or  when 
it  is  equidistant  from  the  edge  at  each  surface  or  is  de- 
viated in  an  equal  amount  at  each  surface,  or  when  the 
angle  of  incidence  (I  R  N)  is  equal  to  the  angle  of  emer- 
gence (V  Y  N')  (Fig.  25).  The  position  of  the  prism 


FIG.  25. — Illustrating  position  of  minimum  refraction  or  deviation.  AB 
and  AC  =  Surfaces.  I  =  Incident  ray  directed  toward  D.  RY=  Course 
of  ray  in  the  prism  and  parallel  to  the  Base  (BC).  V  =  Refracted  Ray  as 
if  it  came  from  I'.  N  and  N'  =  Perpendiculars  or  normals  to  surfaces 
AB  and  AC. 

when  this  occurs  is  spoken  of  as  the  position  of  minimum 
deviation.  Fig.  25  shows  the  prism  BAG.  The  ray 
I  incident  on  the  surface  A  B  at  R  is  refracted  to  Y  and 
emerging  at  Y  is  again  refracted  toward  V.  The  ray 
R  Y  in  the  prism  is  parallel  with  the  base  (B  C) ;  R  and 
Y  are  equidistant  from  the  edge  A. 

Angle  of  Deviation  (Fig.  25). — This  angle  is  formed 
by  the  light  and  is  situated  between  the  directions  of 
the  incident  ray  carried  forward  (I  to  D)  and  the  emer- 
gent ray  (V  to  I')  carried  backward,  it  measures  the  de- 
viation (V  E  D).  In  all  prisms  of  ten  degrees  or  less  the 


REFRACTION   OF    LIGHT  21 

angle  of  deviation  is  slightly  more  than  half  the  angle 
of  the  prism,  but  in  prisms  of  more  than  ten  degrees  the 
angle  of  deviation  is  much  larger. 

Summary. — The  deviation  of  a  ray  of  light  passing 
through  a  prism  is  influenced  chiefly  by  two  factors,  i.e. : 


FIG.  26. — A  and  B,  parallel  rays  entering  the  prism,  are  parallel  as  they 
leave  the  prism. 

1 i )  The  obliquity  of  the  refracting  surfaces :  The  more 
acute  the  edge  angle,  the  less  the  deviation ;  the  greater 
the  edge  angle,  the  greater  the  deviation. 

(2)  The  index  of  refraction  of  the  prism :  The  less  the 
index  of  refraction,  the  less  the  angle  of  deviation;  the 


FIG.  27. — A  and  B  are  divergent  as  they  enter  and  leave  the  prism. 

greater  the  index  of  refraction,  the  greater  the  angle  of 
deviation. 

Prisms  do  not  cause  rays  of  light  to  converge  or  di- 
verge :  Rays  of  light  that  are  parallel  before  refraction  are 


22 


PRISMS 


parallel  after  refraction  (Fig.  26).  Rays  of  light  that 
diverge  (A  B,  Fig.  27)  as  they  enter  a  prism  will  di- 
verge as  they  leave  it.  Rays  of  light  that  converge 


B 


FIG.  28. — A  and  B  are  convergent  as  they  enter  and  leave  the  prism,  these 
rays  cross  at  C. 

(A  B,  Fig.  28)  as  they  enter  a  prism  will  converge  when 
they  leave  it.  Prisms  do  not  form  images.  Prisms 
have  no  foci.  A  prism  and  a  plane  mirror  act  similarly 
upon  rays  of  light,  namely,  if  the  rays  of  light  are  par- 

123      123 


L  D  C 

FIG.  2Q. — PM  =  Plane  Mirror.  L  =  Parallel  rays  1,2,3,  reflected  parallel. 
D  =  Divergent  rays  reflected  divergently.  C  =  Convergent  rays  i  2,  3, 
reflected  convergently. 

allel,  divergent  or  convergent  as  they  fall  upon  a  plane 
mirror  they  will  be  reflected  in  like  manner.  See 
Fig.  29. 


CHAPTER  III 
OPTICAL  EFFECT  OF  A  PRISM 

The  purpose,  or  use,  or  effect  of  a  prism  is  to  make  an 
object  looked  at  through  the  prism  appear  in  a  different 
place  from  that  which  it  really  occupies,  the  prism 
actually  producing  an  optical  illusion.  In  producing 
this  effect  the  object  always  appears  displaced  and  in  a 
direction  always  opposite  to  the  position  of  the  base  of 
the  prism,  namely,  in  the  direction  of  the  edge  of  the 


FIG.  30. — Optical  effect  of  a  prism.    X  appears  in  the  position  of  X'. 

prism.  For  instance,  in  Fig.  30,  rays  of  light  from  the 
object  X  strike  the  prism  at  C,  undergo  minimum  re- 
fraction and  falling  upon  the  retina  of  the  eye  are  pro- 
jected outward  in  the  direction  from  which  they  came 
to  the  eye,  and  the  position  of  X  is  apparently  changed 
to  X',  away  from  the  base  and  toward  the  edge  of  the 
prism. 

Before  proceeding  further,  the  mind  of  the  reader  must 
be  impressed  with  the  fact  that  the  word  edge  and  apex 

23 


24  PRISMS 

as  applied  to  a  prism  are  synonymous  terms,  because 
only  too  frequently  the  student  confuses  these  terms  with 
a  difference.  This  confusion  has  arisen  apparently 
from  the  markings  on  the  circular  or  round  prisms,  but 
by  observing  Fig.  7  the  reader  will  see,  as  already  stated 
in  Chapter  I,  that  the  apex  mark  of  a  circular  or  round 
prism  corresponds  to  a  point  in  the  edge  of  the  original 
square  prism.  If  the  reader  will  also  bear  in  mind  that 


FIG.  31. — H  appears  displaced  toward  the  edge  of  the  prism  and  parallel  to 
the  base-apex  line. 

the  base-apex  line  as  marked  on  the  prism  is  only  a 
guide  and  that  there  are  as  many  imaginary  base-apex 
lines  in  the  prism  as  there  are  imaginary  lines  parallel 
to  the  one  base-apex  line  indicated  on  the  prism,  he  will 
fully  appreciate  the  statement  that  every  point  in  an 
object  seen  through  a  prism  is  displaced  toward  the 
edge  of  the  prism  and  on  a  line  parallel  with  the  base- 
apex  line.  It  is  a  very  erroneous  idea  to  get  the  im- 
pression in  mind  that  because  the  prism  is  round,  the 


OPTICAL  EFFECT   OF  A   PRISM  25 

object  looked  at  through  the  prism  is  displaced  in  all 
its  parts  toward  the  apex  marking  on  the  prism,  as  if  it 
was  to  be  crowded  toward  the  apex  of  an  angle.  In 
Fig.  31  the  letter  H  is  seen  through  the  prism  to  the  right 
of  the  prism  markings  for  the  apex  and  base  and  this  H 
is  displaced  immediately  upward  on  an  imaginary  line 
exactly  parallel  to  the  base-apex  line  and  not  toward  the 
apex  marking  of  the  prism. 

A  straight  line,  at  a  long  distance  viewed  through 
a  strong  prism,  held  base-apex  at  right  angles  to  the 


FIG.  32. — The  straight  line  looked  at  through  the  prism  appears  curved,  the 
concavity  being  toward  the  edge  of  the  prism. 

line,  appears  to  be  curved  and  with  the  concavity 
toward  the  edge  of  the  prism  (Fig.  32).  This  same 
straight  line  viewed  through  the  prism  held  with  the 
base-apex  line  in  the  same  meridian  as  the  line,  does 
not  at  first  appear  displaced,  although  it  is  dis- 
placed, the  displaced  portion  simply  overlying  the 
original  line  and  toward  the  edge  of  the  prism  (Fig.  33), 
making  the  line  appear  a  trifle  darker  and  heavier.  Any 
prism  held  before  the  eye  and  revolved  on  its  plane 
gives  an  object  looked  at  through  the  prism  the  appear- 


26 


PRISMS 


ance  of  moving  in  a  circle  about  its  real  position.  In  a 
right-angled  triangle  prism  (a  principal  section  of  which 
is  a  right-angled  isosceles  triangle)  the  hypotenuse  may 


FIG.  33. — The  straight  line  seen  through  the  prism  on  its  base-apex  line  does 
not  appear  displaced. 

H 


B 


123 

FIG.  34. — The  hypotenuse  HY  acting  as  a  plane  mirror,  producing  total 

reflection. 


act  similar  to  a  plane  mirror  (Fig.  34).  Rays  of  light 
entering  such  a  prism  at  H  B  as  normals  (1,2  and  3) 
fall  upon  the  hypotenuse  (H  Y)  at  an  angle  of  incidence 
of  45  degrees  and  as  this  angle  is  greater  than  the  critical 


OPTICAL   EFFECT    OF  A    PRISM 


27 


angle  (40°  49')  for  crown   glass,  the  rays    are   totally 
reflected.     At  the  same  time  these  rays  are  deviated 


FIG.  35. — Hypotenuse  acting  as  a  plane  mirror. 


FIG.  36. — Showing  how  light  rays  are  bent  by  means  of  prism  angles. 

through  an  angle  of   90  degrees,   consequently   they 
emerge  at  B  Y  as  normals  from  the  other  surface  of 


PRISMS 


the  prism.  See  also  Fig.  35.  This  fact  is  taken  ad- 
vantage of  in  a  mechanical  way  by  the  use  of  these 
and  other  prisms  for  purposes  of  illumination  or  for 
deviating  rays  of  light  into  dark  basements,  stair- 


FlG.  37. — Illustrating  Fresnel's  lighthouse  apparatus. 

ways,  etc.  (Fig  36).  Likewise  prismatic  action  is 
employed  in  the  construction  of  the  lenses  sur- 
rounding the  light  in  a  lighthouse  (Figs.  37  and  38). 
"At  the  center  of  such  an  apparatus  is  a  piano- 


OPTICAL  EFFECT    OF  A   PRISM 


29 


convex  lens,  one  foot  in  diameter,  the  focus  of 
which  corresponds  with  those  of  the  concentric 
lenticular  rings  of  glass  which  surround  it.  The 
rings  are  ground  and  polished  with  great  accuracy  and 
resemble  in  shape  an  ordinary  quoit  and  in  their  refrac- 
tion are  equivalent  to  a  plano-convex  lens  with  its  center 
removed.  Such  lenses  are  so  powerful  that  the  light 
in  a  clear  atmosphere  may  be  seen  at  a  distance  of  fifty 
or  sixty  miles.  The  apparatus  is  octagon  in  shape  and 


FIG.  38. — Lantern  of  a  first-class  lighthouse. 

provided  with  reflecting  mirrors  at  those  parts  above  and 
below  the  light  which  are  out  of  the  range  of  the  lenses. 
The  oil  flame,  as  the  radiant,  is  so  placed  that  when  its 
rays  pass  through  the  lens  and  prism  and  are  reflected 
by  the  mirrors,  they  are  deviated  so  as  to  follow  the 
horizon  very  closely  and  do  not  go  promiscuously  sky- 
ward or  immediately  downward."1 

Corneal  microscopes,  marine  glasses,  and  loupes  are 
now  most  ingeniously  constructed  with  prism  combina- 

1  "Wonders  of  Optics,"  C.  Scribner  &  Co. 


30  PRISMS 

tions  whereby  the  object  is  greatly  enlarged  and  given 
a  flat  surface. 

Prism  Aberration  or  Prismatic  Astigmatism. — A 
divergent  pencil  of  light  passing  through  a  prism  and 
received  into  the  normal  31/2  millimeter  round  pupil 
of  an  eye  is  naturally  projected  toward  the  edge  of  the 
prism  as  just  described,  but  it  is  not  seen  as  a  distinct 
radiant  point ;  it  appears  as  a  point,  however,  with  those 
edges  blurred  or  indistinct  which  coincide  with  the  base- 
apex  line  of  the  prism,  while  the  rays  of  light  which  were 
refracted  in  the  meridian  corresponding  to  the  axis  of 
the  prism  are  distinct ;  in  other  words,  the  rays  which  fall 
upon  the  prism  in  the  vertical  meridian  appear  a  trifle 
further  off  than  the  rays  which  fall  upon  the  prism 
parallel  to  its  edge.  A  circle  viewed  through  a  prism 
appears  very  slightly  oval  on  this  account  and  with  the 
upper  and  lower  edges  faintly  blurred.  This  effect  of  a 
prism  is  spoken  of  as  prism  aberration  or  prismatic 
astigmatism  and  the  interval  between  the  two  focal 
planes  is  known  as  Sturm's  interval.  Very  weak  prisms 
(less  than  2  centrads)  have  such  a  minute  amount  of 
aberration  or  astigmatism  that  it  is  really  infinitesimal 
and  often  non-appreciable.  It  takes  a  strong  prism 
(10  or  more  centrads)  to  demonstrate  abberration  and 
as  strong  prisms  are  seldom  prescribed  this  astigmatic 
effect  need  not  have  further  consideration  at  this  time. 

Metamorphopsia. — Rotating  a  prism  on  its  axis  or  on 
its  base-apex  line  as  the  observer  looks  through  it  at  an 
object,  the  object  becomes  distorted  and  this  distortion 
is  spoken  of  as  metamorphopsia ;  for  instance,  holding  a 
strong  prism  base  downward  axis  90°  before  the  eye  and 


OPTICAL  EFFECT    OF  A    PRISM 


PRISMS 


OPTICAL  EFFECT    OF  A   PRISM 


33 


looking  at  an  object  (window  A  in  Fig.  39)  it  naturally 
appears  displaced  upward  (B  in  Fig.  39)  then  tilting 
the  edge  forward  toward  the  object  (dotted  prism,  same 
figure),  thus  bringing  the  base  toward  the  observer's  eye, 
gives  B  the  appearance  of  being  displaced  still  further 
upward  (C  in  Fig.  39)  and  at  the  same  time  the  object 
(window)  is  very  much  elongated  (magnified)  vertically, 
the  horizontal  width  remaining  unchanged. 

Holding  a  strong  prism  base  downward  axis  90°  be- 
fore the  eye  and  tilting  the  base  toward  the  object  (bring- 
ing the  edge  toward  the  observer's  eye)  (Fig.  40)  gives 
the  displaced  object  (B)  the  appearance  of  being  still 


FIG.  41. 


FIG.  42. 


further  displaced  from  B  to  C  and  very  much  reduced 
in  size  (minified)  in  the  vertical  meridian  and  the 
horizontal  width  of  the  object  remains  unchanged. 
Rotating  a  prism  to  the  right  on  its  base-apex  line  as  it  is 
held  base  downward  axis  90°  before  the  eye,  and  the  eye 
views  a  square  through  the  prism,  the  right  side  of  the 
square  appears  to  move  upward  (Fig.  41)  and  if  the 
prism  is  rotated  to  the  left,  the  left  side  appears  to  move 
upward  (Fig.  42).  In  each  instance  the  square  object 
has  a  distortion  resembling  a  rhombus. 

Dispersion  of  Light. — When  a  beam  of  solar  light 
(B  in  Fig.  43)  is  made  to  pass  through  a  prism  of  rock 
crystal  or  flint  glass  it  is  broken  up  or  divided  into  its 

3 


34 


PRISMS 


constituent  parts  and  this  phenomenon  is  spoken  of  as 
dispersion.  This  beam  of  light  directed  toward  E,  if 
intercepted  by  a  screen  will  be  seen  as  a  colored  image, 
known  as  the  solar  spectrum  at  C.  This  image  is 
rounded  at  the  ends  and  the  colors  seen  are  red,  orange, 
yellow,  green,  blue,  indigo  and  violet  in  the  order  named 
-^violet  being  the  most  refrangible  and  red  the  least. 


FIG.  43. — Dispersion  or  the  production  of  a  spectrum  by  a  flint  glass  or  rock 

crystal  prism. 

These  colors  do  not  have  sharp  lines  of  demarcation, 
but  blend  into  each  other.  Dispersion  plays  but  an 
infinitesimal  part  in  ophthalmology  for  the  reason  that 
strong  prisms  are  not  prescribed  and  furthermore  the 
prisms  in  the  trial  case  are  of  crown  glass. 

COMPARING  THE  ACTION  OF  A  PRISM,  A  SPHERE  AND 
A  CYLINDER 

A  Prism. — Looking  at  a  straight  line  through  a  prism 
held  in  its  position  of  minimum  deviation  and  its  base- 


OPTICAL  EFFECT   OF  A   PRISM 


35 


apex  line  exactly  at  right  angles  to  a  line,  the  line  appears 
displaced  in  the  direction  of  the  edge  of  the  prism  (Fig. 
32)  and  this  exact  amount  of  displacement  never  changes 
so  long  as  the  prism  and  line  are  kept  at  a  definite  dis- 
tance apart,  no  matter  how  far  to  the  right  or  to  the 
left  the  prism  may  be  moved.  As  already  stated,  when 
the  prism  is  held  so  that  the  base-apex  line  coincides 
with  the  straight  line  a  displacement  of  the  line  exists 
but  is  not  always  apparent,  because  in  this  position  the 
displaced  portion  is  superimposed  on  the  original  line 
(Fig-  33)- 


FIG.  44. 

The  Optic  Center  of  a  Convex  Lens. — Looking  at  a 
vertical  straight  line  and  passing  a  convex  lens  before  the 
eye  from  left  to  right  has  the  effect  of  displacing  toward 
the  right  edge  of  the  lens  that  portion  of  the  line  seen 
through  the  lens  (Fig.  44)  and  as  the  lens  is  slowly 
moved  still  further  to  the  right,  the  displaced  portion  of 
the  line  will  finally  coincide  with  the  original  straight 


36  PRISMS 

line  making  one  continuous  line  through  the  lens  (Fig. 
45).  Marking  this  straight  line  on  the  surface  of  the 
lens,  and  then  turning  the  lens  to  the  opposite  meridian 


FIG.  45. 

and  repeating  the  examination,  and  marking  the  lens  as 
before,  the  optic  center  will  be  in  the  lens  beneath  the 
point  of  intersection  of  the  two  lines  (Fig.  46). 


FIG.  46. 


A  Convex  Sphere. — Objects  viewed  through  a  con- 
vex lens  as  it  is  moved  before  the  eye,  from  left  to  right 
and  right  to  left  or  up  and  down,  appear  to  move  in  an 


OPTICAL   EFFECT    OF   A   PRISM 


37 


opposite  direction  to  that  in  which  the  lens  is  moved. 
The  weaker  the  lens,  the  slower  the  object  appears  to 
move;  and  the  stronger  the  lens,  the  faster  the  apparent 
movement  of  the  object.  A  convex  lens  being  a  magni- 
fier, has  the  effect  of  making  objects  appear  larger  and 
closer  when  it  is  moved  away  from  the  observer's  eye; 
or  if  brought  toward  the  eye,  objects  already  enlarged 
appear  smaller  and  more  distant. 

A  Concave  Sphere. — When  a  concave  sphere  is 
moved  before  the  eye  from  left  to  right  and  right  to  left 


FIG.  47. 

or  up  and  down,  objects  appear  to  move  in  the  same 
direction  as  that  in  which  the  lens  is  moved.  A  concave 
lens  being  a  minifier,  makes  objects  appear  smaller  and 
more  distant  as  the  glass  is  moved  away  from  the  eye, 
and  if  brought  closer  to  the  eye,  it  makes  objects  appa- 
rently small  appear  somewhat  larger  and  nearer.  Look- 
ing at  a  straight  edge  or  line  through  a  concave  sphere, 
and  passing  the  lens  from  left  to  right,  the  portion  of  the 
line  seen  through  the  lens  appears  displaced  toward  the 


38  PRISMS 

center  of  the  lens  (Fig.  47),  and  as  the  lens  is  still  further 
moved  to  the  right,  the  displaced  portion  of  the  line 
finally  coincides  with  the  original  straight  edge,  as  in 

Fig.  45- 

The  optic  center  of  a  concave  lens  is  found  in  the  same 
way  as  finding  the  center  of  a  convex  lens. 

A  Convex  Cylinder. — When  a  convex  cylinder  is 
moved  in  front  of  the  eye  in  the  direction  of  its  axis, 
objects  looked  at  do  not  change  their  positions;  but 
when  the  lens  is  moved  in  the  direction  opposite  to  its 
axis,  the  movement  of  the  object  is  the  same  as  that  of  a 


FIG.  48. 

convex  sphere.  Looking  at  a  straight  edge  through  a 
convex  cylinder,  and  rotating  it,  has  the  effect  of  dis- 
placing away  from  its  axis  that  portion  of  the  straight 
edge  seen  through  the  lens  (Fig.  48). 

A  Concave  Cylinder. — When  a  concave  cylinder  is 
moved  in  front  of  the  eye  in  the  direction  of  its  axis, 
objects  looked  at  do  not  change  their  positions;  but 
when  the  lens  is  moved  in  the  direction  opposite  to  its 
axis,  the  movement  of  the  object  is  the  same  as  that  of  a 
concave  sphere.  Looking  at  a  straight  line  through  a 


OPTICAL   EFFECT    OF  A    PRISM  39 

concave  cylinder,  and  rotating  it,  has  the  effect  of  dis- 
placing toward  its  axis  that  portion  of  the  straight  line 
seen  through  the  lens  (Fig.  49).  A  circle  viewed 


FIG.  49. 


through  a  strong  concave  cylinder  appears  as  an  oval 
with  its  long  diameter  corresponding  to  its  axis  (Fig.  50). 


FIG.  50. 

A  circle  viewed  through  a  strong  convex  cylinder  ap- 
pears as  an  oval  with  its  long  diameter  opposite  to  its 
axis. 


CHAPTER  IV 

PRISM  NOMENCLATURE.     DENNETT'S   METHOD. 

PRENTICE'S  METHOD  AND  NEUTRALIZING 

PRISMS 

Numbering  of  Prisms.— Formerly  prisms  were 
numbered  by  their  refracting  angles  or  the  edge  angle 
formed  between  the  two  refracting  surfaces.  Such 
prisms  were  known  as  one  degree  (i°),  two  degrees  (2°), 
three  degrees  (3°),  etc.  Early  trial  cases  had  these 
prisms  numbered  in  this  way,  sometimes  as  high  as  num- 
ber twenty-four.  They  were  often  spoken  of  as  num- 
ber one,  number  two,  number  three,  etc.  The  unit 
(number  one)  or  any  degree  numbered  prism  does  not, 
unfortunately,  signify  or  designate  definitely  the  amount 
of  deviation  a  ray  of  light  will  undergo  in  passing 
through  such  a  numbered  prism;  the  degree  simply 
designates  the  inclination  or  angle  formed  by  the  sides 
of  the  prism.  It  will  be  noted  later  that  this  method  of 
numbering  prisms  was  most  unsatisfactory  because  it 
did  not  indicate  the  angle  of  deviation  which  the  ray  of 
light  would  make  when  it  passed  through  the  prism. 
Or  to  state  it  in  another  way,  the  degree  notation  of 
prisms  did  not  inform  the  surgeon  just  how  much  such 

40 


PRISM   NOMENCLATURE  41 

a  prism  would  deviate  a  ray  of  light  when  in  its  position 
of  minimum  deviation  (Chapter  II,  also  Fig.  25). 

When  referring  to  the  strength  of  a  prism  it  is  always 
better  to  mention  its  deviating  power;  for  instance,  a 
number  4  prism  does  not  convey  the  proper  meaning 
except  that  the  surfaces  of  such  a  prism  have  an  apical 
angle  of  four  degrees,  and  therefore  if  we  wish  to  say 
that  a  4  prism  will  deviate  a  ray  of  light  four  degrees, 
we  must  insert  the  letter  "d"  after  the  4,  which  would  be 
"4  d  prism."  A  change  from  this  " degree"  nomen- 
clature of  prisms  was  urged  by  Dr.  Edward  Jackson 
(now  of  Denver,  Colorado)  before  the  Ninth  Inter- 
national Medical  Congress  and  he  very  wisely  and  prop- 
erly recommended  that  prisms  be  numbered  or  marked 
according  to  their  power  of  deviating  rays  of  light  and 
the  edge  angle  to  be  ignored. 

An  instrument  for  measuring  the  edge  angle  of  the 
prism  is  made  by  the  Geneva  Optical  Company  and 
called  a  "prism  measure,"  but  it  is  of  no  use  to  the 
oculist  as  it  does  not  register  the  deviating  power  of  the 
prism.  It  is  an  instrument,  however,  which  the  optician 
can  use  to  advantage. 

Since  Dr.  Jackson's  recommendation  for  a  new  or 
exact  prism  nomenclature,  two  methods  have  come  into 
use,  namely,  Dennett's  Method  and  Prentice's  Method. 

The  size  of  the  angle  of  deviation  produced  by  a  ray 
of  light  passing  through  a  prism  measures  the  strength 
or  the  effect  of  the  prism  and  it  is  this  angle  which  has 
given  us  the  new  nomenclatures  now  to  be  described. 

Dr.  Dennett's  Method. — TheCentrad.  Abbreviated 
by  an  inverted  Greek  letter  D  (Delta)  V.  The  unit  of 


42  PRISMS 

this  method  (one  centrad)  is  a  prism  which  will  deviate 
a  ray  of  light  the  one-hundredth  part  of  the  arc  of  the 
radian.  (See  Radian,  Chapter  II.)  This  is  an  arc 
measurement  and  the  arc  of  the  radian  always  equals  a 
little  more  than  fifty-seven  degrees  (57-295+°).  In 
Fig.  51  R  A  and  R  C  are  radii  of  curvature,  A  C  is  the 
arc  of  the  radian  and  is  equal  in  length  to  either  R  A 
or  R  C.  This  arc  is  now  divided  into  100  equal  parts. 


R  A 

FIG.  51. — Illustrating  Dennett's  method  of  numbering  prisms. 

A  prism  base  up  axis  90°  at  the  center  of  curvature  (R) 
which  will  deviate  a  ray  of  light  just  one-hundredth 
part  of  this  arc  is  a  unit  prism  of  one  centrad  (iv) 
and  in  its  deviating  power  equals  therefore  the  one- 
hundredth  part  of  57.295  degrees,  or  0.57295  of  a 
degree.  This  unit  power  tells  at  once  the  deviating 
power  of  any  number  of  centrads  by  simply  multiplying 
this  unit  power  (0.57295)  by  the  number  of  centrads  in 


PRISM    NOMENCLATURE 


43 


the  prism;  for  instance,  a  five  centrad  prism  (5V)  will 
deviate  a  ray  of  light  5X0.57295  which  equals  2.8647°, 
and  a  ten  centrad  prism  (iov)  will  deviate  a  ray  of 
light  10X0.57295  which  equals  5.7295°  etc. 

Mr.  Charles  F.  Prentice's  Method. — Prism-diopter 
or  prism-dioptry.  Abbreviated  by  the  Greek  letter  D 
(Delta)  A-  The  unit  of  this  method  (one  prism-diop- 


FIG.  52. — Illustrating  Prentice's  method  of  numbering  prisms. 


ter)  is  a  prism  which  will  deviate  a  ray  of  light  just  one 
centimeter  for  each  meter  of  distance  that  it  travels. 
The  prism-diopter  is  strictly  a  tangent  measurement 
(Fig.  52).  As  the  deviation  of  a  prism-diopter  is 
always  one  centimeter  for  each  meter  of  distance 
then  one  prism-diopter  will  deviate  a  ray  of  light  two 
centimeters  for  two  meters  of  distance,  three  centi- 


44 


PRISMS 


I    I    I   I 


H  . 

« 

D 


PRISM    NOMENCLATURE 


45 


meters  for  three  meters  of  distance,  four  centimeters 
for  four  meters,  etc.  (Fig.  53). 

The  comparative  values  of  centrads  and  prism  diop- 
ters is  quite  uniform  up  to  20,  but  above  20  the  centrad 
becomes  the  stronger  (Fig.  54).  As  the  every-day  use 


50° 


FIG.  54. — Comparing  Dennett's  and  Prentice's  methods  of  numbering 
prisms. 


of  prisms  seldom  calls  for  a  prism  stronger  than  20 
(centrad  or  prism-diopter)  the  surgeon  need  not  be 
annoyed  with  any  distinction  between  the  two  nomen- 
clatures until  he  passes  to  a  prism  stronger  than  20. 
The  following  table  is  self  explanatory. 


46 


PRISMS 


TABLE  SHOWING  THE  EQUIVALENCE  OF  CENTRADS  IN  PRISM-DIOPTERS  AND 
IN   DEGREES  OF  THE  REFRACTING  ANGLE  (INDEX  OF  REFRACTION    1.54) 


Centrads 

Prism-diopters 

Refracting  angle 

i. 

i  . 

i°.oo 

2. 

2  .OOOI 

2°.  12 

3- 

3.0013 

3°-i8 

4- 

4.0028 

4°-23 

5- 

5-0045      „'. 

5°.  28 

6. 

6.0063 

6°.  32 

7- 

7.0115 

7°  -35 

8. 

8.0172 

8°.  38 

9- 

9.0244 

9°  -39 

10. 

10.033 

10°.  39 

u. 

ii  .044 

"°-37 

12. 

12.057 

12°.  34 

*3- 

J3-074 

13°.  29 

14. 

14.092 

14°  -23 

IS- 

15.114 

15°.  16 

16. 

16.138 

i6°.o8 

i7- 

17.164 

i6°.98 

18. 

18-196 

17°.  85 

19. 

19.230 

i8°.68 

20. 

20.270 

19°  -45 

25- 

25-55 

23°  -43 

30- 

30-934 

26°.  81 

35- 

36-50 

29°.  72 

40. 

42.28 

32°.  18 

45- 

48.30 

34°.  20 

So- 

54-5J4 

35°  -94 

60. 

68.43 

38°.  31 

70. 

84.22 

39°  -73 

80. 

IO2  .96 

40°.  29 

90. 

I26.OI 

40°.  49 

IOO. 

155-75 

39°  -i4 

"The  actual  difference  between  corresponding  num- 
bers of  the  two  scales  is  the  difference  between  the 


PRISM   NOMENCLATURE  47 

tangent  and  the  arc  of  the  same  number  of  hundredth- 
radians.  The  practical  difference  within  the  limits  of 
actual  use  is  hard  to  see."1 

"In  1891  the  Ophthalmic  Section  of  the  American 
Medical  Association  passed  a  resolution  recommending 
the  adoption  of  the  centrad  unit  and  scale  and  equally 
with  that  up  to  20,  the  prism-diopter."1 

Neutralization  of  Prisms. — The  word  neutraliza- 
tion as  used  in  opththalmology  means  to  counteract 
or  render  inert  or  it  may  be  described  as  antagonizing 
or  as  an  opposite  effect.  For  instance,  if  a  ray  of 
light  passing  through  a  prism  is  deviated  two  centi- 
meters at  one  meter  of  distance,  then  to  neutralize  this 
effect  or  antagonize  this  deviation  it  will  be  necessary 
to  find  a  prism  of  equal  strength  and  place  it  with  its 
base  to  the  apex  of  the  other  prism,  or  to  be  able  to  neu- 
tralize a  prism  all  that  is  necessary  is  to  find  its  numeric 
strength.  To  do  this,  the  prism  to  be  tested  must  be 
held  in  its  position  of  minimum  deviation  with  base- 
apex  line  at  right  angles  and  over  a  series  of  numbered 
parallel  straight  lines  separated  by  an  interval  of  one 
centimeter  (or  multiple  or  fraction  thereof)  and  note 
the  amount  of  displacement  that  results  when  the  prism 
is  held  at  a  distance  in  meters  (or  multiple  or  fraction 
of  a  meter)  according  to  the  interval  between  the  lines. 
Fig.  55  shows  a  series  of  vertical,  parallel  straight  lines 
one-half  centimeter  apart  and  numbered  from  o  to  9. 
An  X  is  placed  at  the  foot  of  the  zero  line.  All  the 
parallel  lines  are  at  right  angles  to  the  black  line  B  L. 

1  William  S.  Dennett,  M.  D.:  "System  of  Diseases  of  the  Eye,"  Norris 
and  Oliver,  Vol.  II,  page  150. 


PRISMS 

9876543210 


B 


9876543210 


B 


FIG.  55. — Author's  method  of  estimating  the  strength  of  a  prism. 


PRISM    NOMENCLATURE 


49 


Holding  a  prism  base  to  the  right,  axis  180°,  at  a  dis- 
tance of  50  centimeters  (half  a  meter)  from  the  lines 
(as  the  lines  are  one-half  centimeter  apart)  and  look- 
ing through  the  prism  at  X  on  the  zero  line  and  also 
at  the  line  B  L,  it  will  be  seen  that  the  X  line  has  been 
displaced  to  the  line  to  the  left  corresponding  to  the 

9876543210 


FIG.  56. 

number  of  centrads  or  prism-diopters  in  the  prism 
which  is  being  tested — in  this  instance,  three.  The 
displaced  portion  of  the  B  L  line  is  carried  forward 
and  superimposed  upon  itself,  otherwise  it  would 
appear  out  of  alignment,  if  the  prism  was  not  held  with 
the  base-apex  line  corresponding  to  the  B  L  line,  as 
shown  in  Fig.  56.  If  the  zero  line  (X)  had  been  dis- 


50  PRISMS 

placed  between  the  lines  marked  2  and  3  then  the 
number  of  the  prism  would  have  been  more  than  two 
or  less  than  three  centrads  or  prism-diopters.  If  it 
has  been  displaced  to  the  line  marked  5  then  it  would 
have  been  a  5  prism,  etc.  It  might  be  just  as  well 
to  remind  the  reader  that  it  makes  no  difference  at 
what  distance  his  eye  may  be  from  the  prism  while 
making  this  test,  but  it  is  of  the  utmost  importance  to 

987654  3  2101234567S9 


A 

O 

1 

1 

-i 

1 

K 

-  fi 

9876543210123456789 
FIG  57. — Prismometric  scale  of  Charles  F.  Prentice.1 

hold  the  prism  in  the  manner  mentioned  and  at  the 
exact  distance  in  meters  or  fraction  of  a  meter,  corre- 
sponding to  the  centimeter  interval  between  the  lines. 
To  find  the  strength  of  a  prism.  Mr.  Prentice,  who  pro- 
posed the  prism-diopter,  recommends  using  a  graduated 
card  having  lines  upon  it  separated  by  an  interval  of 
six  centimeters  and  this  of  course  must  be  placed  at  a 
distance  of  six  meters  and  used  as  in  the  former  test. 
This  scale  is  exact  and  called  by  its  author  a  "prismo- 

1  Copyright,  see  footnote  page  98. 


PRISM   NOMENCLATURE  51 

metric  scale"  (Fig.  57).    This  scale  may  also  be  used 
for  muscle  testing  and  is  described  in  Chapter  VII. 

A  prism  may  be  neutralized  by  placing  another 
numbered  prism  from  the  trial  case  in  opposition  to  it, 
the  base  of  one  to  the  edge  of  the  other  (Fig.  58),  so 
that  in  looking  through  the  two  prisms  at  a  straight 
line,  no  matter  at  what  distance,  the  straight  line  will 
continue  to  make  a  straight  line.  The  strength  of  the 
neutralizing  prism  will  correspond  to  the  number  of 
the  prism  being  neutralized.  As  the  prisms  in  the 


FIG.  58. — Neutralization  of  prisms. 

trial  case  occasionally  get  loose  in  their  individual 
frames  or  cells,  it  will  be  well  for  the  surgeon  to  test 
the 'prism  in  the  manner  described  in  Fig.  55  to  make 
sure  that  they  are  properly  placed.  The  base-apex 
line  should  coincide  with  the  B  L  line  and  with  the 
makings  on  the  frame.  Dr.  Ziegler's  prism  scale  (Fig. 
59)  is  an  excellent  one.  The  directions  for  its  use  are 
as  follows: 

This  prism  scale  is  to  be  used  at  a  distance  of  a 
quarter  meter,  but  a  larger  one  for  use  at  two  meters 
is  preferable  as  the  possibility  of  error  is  much  less. 
To  use  the  scale  close  one  eye,  and  with  the  other  look 
at  the  scale  both  through  the  prism  and  over  it.  A 


PRISMS 


20  18  16  14  12  10  8  6  4  2 


19 


17 


15 


13 


11 


-10 


FIG.  59. — Prism  scale  of  Dr.  Lewis  S.  Ziegler. 


PRISM   NOMENCLATURE  53 

comparison  of  these  two  views  gives  the  required  regis- 
tration. Each  field  must  contain  either  the  indicator 
singly  or  the  numbered  gradations  singly;  the  fields 
being  in  conjunction  at  the  margin  of  the  lens. 

Rotate  the  prism  until  the  base  line  seen  through  the 
prism  is  continuous  with  the  base  line  of  the  scale. 
Always  keep  the  plane  of  the  prism  parallel  with  that 
of  the  scale,  and  on  a  level  with  it.  The  index  line  will 
be  displaced  along  the  scale  until  the  indicator  stands 
opposite  the  proper  numbered  gradation.  By  moving 
the  prism  up  and  down  along  this  gradation,  it  can 
be  seen  whether  the  index  line  accurately  coincides  or 
not. 


CHAPTER  V 
COMBINED    PRISMS 

Combined  Prisms. — Any  two  prisms  of  the  same 
strength  with  the  base  of  each  against  the  edge  of  the 
other  will  neutralize  each  other  and  the  effect  will  be 
negative.  See  neutralization  of  prisms,  Chapter  IV, 

Fig.  58- 

Any  two  prisms  of  the  same  or  different  strength 
with  the  base  of  one  to  the  base  of  the  other  will  equal 
the  effect  of  a  single  prism  of  the  combined  strength 


FIG.  60. — Two  prisms  in  apposition.     Base  and  edge  of  one  to  the  base  and 
edge  of  the  other. 

of  the  two  (Fig.  60).  Any  two  prisms,  each  less  than 
5V ,  of  the  same  strength  held  in  apposition  and  with 
their  base-apex  lines  at  right  angles  to  each  other  (Fig. 
61)  will  equal  or  be  equivalent  to  a  single  prism  one  or 
two  units  stronger  than  one  of  the  prisms,  with  its 
base  midway  of  the  two  bases.  For  instance,  5  prism- 

54 


COMBINED    PRISMS  55 

diopters  base  down  axis  45  combined  with  a  5  prism- 
diopter  base  down  axis  135  will  equal  a  7  prism-diopter 
base  down  axis  90°.  This  is  a  very  close  equivalent 
in  effect  and  applies  to  pairs  of  prisms  as  high  as 
5  centrads  or  5  prism-diopters,  but  when  pairs  of 
prisms  as  strong  as  15  are  used  the  effect  is  much  greater 
and  with  i5v  the  effect  will  approximate  a  single  21 
prism-diopter. 

That  the  reader  may  fully  appreciate  these  statements, 
he  should  make  these  tests  for  himself  and  in  this  way 


Prism 


FIG.  61. — Two  prisms  of  the  same  strength  superimposed.     One  base  down 
axis  45  and  the  other  base  down  axis  135. 

become  familiar  with  the  prism  effects  or  equivalents. 
The  following  description  will  also  be  of  assistance: 

Fig.  62  shows  a  single  8  prism-diopter  held  about 
10  inches  away  from  and  directly  over  the  word 
"Prism."  (Both  eyes  of  the  observer  must  be  kept 
open  to  make  this  test.)  The  base-apex  line  is  at 
axis  45°  and  base  downward.  The  word  "Prism" 
now  seen  through  the  prism  appears  displaced  upward 
to  the  right  on  the  base-apex  line,  on  axis  45°.  Likewise 


PRISMS 


Fig.  63  shows  another  prism  of  same  strength  held  in 
the  same  manner  over  another  word  "Prism"  and  the 
base  of  the  prism  downward  on  axis  135°.  It  pro- 


Prism 


FIG.  62. 


duces  a  similar  amount  of  displacement  of  the  word 
"Prism,"  upward  and  to  the  left  on  axis  135°.  If 
these  two  prisms  are  now  superimposed  in  their  re- 


Prism 


FIG.  63. 


spective  positions  (45°  and  135°)  as  shown  in  Fig.  61, 
and  the  word  "Prism"  as  also  shown  in  Fig.  61,  is  now 
looked  at  through  this  combination,  the  word  "Prism" 


COMBINED    PRISMS  57 

will  appear  displaced  upward  on  axis  90°  and  the  effect 
thus  produced  is  equivalent  to  a  single  11  prism  base 
down  axis  90°,  Fig.  64. 

As  just  stated  and  illustrated  (Fig.  58),  any  two  prisms 
of  the  same  strength  with  the  base  of  each  to  the  apex  of 
the  other,  neutralize  each  other  and  the  effect  is  negative, 
but  if  these  two  prisms  still  held  in  opposition  are  now 
revolved  in  opposite  directions  at  an  equal  rate  of 
speed,  the  effect  produced  is  that  of  a  prism  gradually 


Prism 
FIG.  64. 

growing  stronger  and  stronger  in  its  effect  until  the 
bases  of  the  two  prisms  become  superimposed  and  the 
resulting  effect  will  be  the  combined  strength  of  the 
two  prisms  (Fig.  60) 

At  first  thought  the  student  will  naturally  imagine 
that  such  a  mechanism  (Fig.  61)  must  produce  two 
images  (diplopia)  of  any  object  looked  at,  but  the  error 
of  this  supposition  will  be  dispelled  by  reference  to 
Fig.  6 1  and  by  making  the  tests  for  himself.  Sir  John 
Herschel  was  the  first  to  show  the  effect  of  combining 
two'prisms  and  by  rotating  them  in  opposite  directions  to 


PRISMS 


obtain  the  effect  of  a  single  prism  of  increasing  strength 
up  to  the  combined  value  of  the  two. 

Crete  of  Paris  was  the  first  to  bring  forth  an  instru- 
ment which  gave  practical  use  to  two  superimposed 


FIG.  65. — Front  view  of  tne  revolving  prisms  as  arranged  by  Crete. 

prisms.  It  is  called  "Crete's  Prism"  or  the  "Prisme 
mobile."  See  Fig.  65.  These  two  prisms  are  mounted 
in  a  circular  cell  with  a  straight  handle.  This  handle 
contains  a  slot  through  which  travels  a  movable  button 


COMBINED    PRISMS  59 

adjusted  to  the  prisms  so  that  on  pushing  the  button 
upward  or  downward  the  prisms  are  made  to  revolve 
in  opposite  directions  at  an  equal  rate  of  speed.  The 
figures  on  the  handle  opposite  the  gauge  record  the 
strength  of  the  prism  thus  produced. 

The  handle  of  the  "Crete  prism  and  also  the  posi- 
tion of  its  degree  markings  interfere  with  its  usefulness 
and  make  it  cumbersome  for  every-day  practice  ;ns. 
fact  the  instrument  is  rather  obsolete  for  these  reaso  in 
The  most  adaptable  form  of  Crete's  prism  which  does 
away  with  the  handle  is  that  of  Dr.  S.  D.  Risley,  known 


FIG.  66. 

as  the  "Rotary  prism,"  Fig.  66.  This  apparatus  which 
may  be  used  in  the  trial-frame  is  composed  of  two  super- 
imposed prisms  of  15  prism-diopters  or  15  centrads 
each,  and  mounted  in  a  cell  of  the  size  of  the  trial  lens. 
By  means  of  a  milled  edged  screw  these  prisms  are 
made  to  revolve  so  that  in  the  position  of  zero  they 
neutralize  each  other,  and  when  revolved  over  each 
other  the  prism  strength  gradually  increases  until  the 
bases  of  the  two  prisms  superimpose,  equalling  (15  +  15) 
30  centrads,  The  prism  strength  is  indicated  by  a 


6o 


PRISMS 


pointer  directed  to  the  scale  on  the  periphery  of  the 
cell.  "Rotary  prisms"  are  made  in  two  strengths, 
one  contains  two  10  prisms  and  the  other,  as  just  de- 
scribed, two  1 5  prisms.  See  Chapter  on  Muscle  Testing. 


FIG.  67. — Jackson's  triple  prism. 

Jackson's  triple  prism  (Fig.  67)  is  very  similar 
to  the  Cre"te  or  Risley  prism.  It  contains  three  prisms, 
as  its  name  implies;  one  of  these  is  stationery  and  the 
other  two  revolve. 


CHAPTER  VI 

COMBINING  A  PRISM  WITH  A  SPHERE,  CYLINDER  OR 
SPHERO -CYLINDER 

Before  taking  up  the  consideration  of  these  combina- 
tions, the  reader  must  be  acquainted  with  the  following: 

The  geometric  center  of  a  lens  is  a  point  midway 
of  the  diameters  of  the  surface;  therefore  there  is  a 
geometric  center  for  each  surface  and  these  are  super- 
imposed. As  the  geometric  center  is  always  con- 


FJG.  68. — The  dot  in  G  at  the  point  of  crossing  of  BB  with  AA  indicates  the 
optic  and  geometric  centers  superimposed. 

trolled  by  the  midpoint  of  the  diameters,  it  is  easily 
located.  Fig.  68  shows  a  circle  which  may  be  considered 
as  the  outline  or  contour  of  a  lens.  A  A  and  BB  are  di- 
ameters. The  dot  in  the  G  is  the  midpoint  of  these 
diameters  and  is  therefore  the  geometric  center.  As 

61 


62 


PRISMS 


another  illustration,  see  Fig.  69.  This  is  the  outline  of 
a  spectacle  lens;  AA  and  BB  represent  the  two  chief 
diameters  and  the  dot  in  the  G  is  the  midpoint  of  these 
diameters  and  hence  is  the  geometric  center.  Also 
see  dot  on  surfaces  of  lens  pictured  in  Fig.  70. 


FIG.  6g. — Dot  in  G  =  geometric  center. 


Axial  Ray  <- 


FIG.  70. — Dot  in  O  =  Optic  center.     Dots  =  Geometric  centers. 

Optic  Center. — This  term  is  used  synonymously 
with  nodal  point,  but  it  is  not  and  must  not  be  confused 
with  the  geometric  center.  The  optic  center  is  the 
point  where  secondary  rays  cross  the  axial  ray  (dot 


COMBINING   A    PRISM    WITH   A    SPHERE  63 

in  the  O,  Fig.  70).  Rays  of  light  crossing  the  optic 
center  in  thin  lenses  are  not  considered  as  undergoing 
refraction  (S  A  in  Fig.  70).  The  optic  center  is  always 
a  fixed  point  and  may  be  located  at  any  part  of  the  lens 
or  at  an  imaginary  point  beyond  its  edge.  In  Fig. 
70  the  optic  and  geometric  centers  coincide,  but  in 
Fig.  71  they  do  not  coincide.  To  summarize,  the  optic 
center  is  always  at  the  thickest  part  of  a  convex  lens 
and  the  thinnest  part  of  a  concave  lens. 


FIG.  71. 


True  Center  of  a  Lens. — A  lens  is  said  to  be  cen- 
tered when  the  optic  and  geometric  centers  coincide 
or  are  both  on  the  visual  axis  (Figs.  70  and  72). 

When  the  optic  and  geometric  centers  do  not  coincide 
then  such  a  lens  has  a  prism  effect  or  combination, 
hence  (Fig.  71) 

(1)  The  nearer  the  optic  and  geometric  centers  coin- 
cide with  or  approximate  the  axial  ray  the  less  the  pris- 
matic effect. 

(2)  The  further  apart  the  optic  and  geometric  cen- 
ters the  greater  the  prismatic  effect  (Fig.  71). 

(3)  In  weak  lenses  or  lenses  with  long  radii  of  curva- 


64 


PRISMS 


ture,  a  slight  lateral  displacement  of  the  optic  center 
produces  but  little  prismatic  effect. 

(4)  In  strong  lenses  or  those  with  short  radii  of  cur- 
vature, a  slight  lateral  displacement  of  the  optic  center 
from  the  geometric  center  will  produce  considerable 
prismatic  effect. 

Or  3  and  4  may  be  restated  briefly  ',i.e.,  a  strong  lens 
requires  less  lateral  displacement  of  the  optic  center 
from  the  geometric  center  than  a  weak  lens  to  obtain 
the  same  amount  of  prismatic  effect  in  each. 


-V-A: 


FIG.  72. 

Unless  otherwise  prescribed,  every  lens  placed 
before  the  patient's  eye  is  supposed  to  have  the  optic 
and  geometric  centers  coincide  with  the  visual  axis  of 
the  eye  (Fig.  72),  then  there  will  not  be  any  prismatic 
effect.  If  there  is  any  departure  from  this  correct 
position  for  the  lens  and  the  eye  together,  then  a  pris- 
matic effect  is  produced  and  its  amount  is  in  proportion 
to  the  displacement  or  separation  and  the  strength  of 
the  lens  in  use  (Fig.  71). 

Decentering  (Decentring)  a  Lens. — This  may  be 
described  as  having  the  optic  center  of  a  lens  laterally 
displaced  from  the  geometric  center,  so  that  the  eye 


COMBINING   A    PRISM    WITH   A    SPHERE  65 

looking  through  such  a  lens  sees  through  the  geometric 
center  but  not  the  optic  center  (Fig.  71).  In  other 
words  the  geometric  center  is  on  the  visual  axis  but  the 
optic  center  is  to  one  side  (Fig.  71). 

A  decentered  lens  may  therefore  be  described  as  one 
whose  optic  and  geometric  centers  do  not  coincide 
(Figs.  71,  75,  76,  77  and  78). 

When  ordering  a  prism  in  combination  with  a  lens 
the  prescriber  may  write  his  prescription  out  in  full 


FIG.  73. — Dots  at  GG  =  Geometric  centers.     Dot  in  O  =  Optic  center  of 
this  combination. 

or  he  may  specify  that  the  lens  is  to  be  decentered. 
For  instance  +4  sphere  O  4A  base  down  axis  90°. 
This  is  equivalent  to  a  piano  +2  sphere1  on  each 
surface  of  the  4  prism  (Fig.  73). 

The  optician  would,  however,  take  a  +  4  sphere  (in 
the  rough2  as  he  calls  it)  and  grind  or  polish  the 
other  surface  at  an  angle  as  indicated  by  the  straight 
dotted  line.  See  Fig.  74.  The  angle  at  which  he 

1  It  might  be  well  to  mention  that  the  optician  carries  spheric  lenses  in 
stock  that  are  round  or  circular  in  contour  and  cylinders  that  are  square. 

2  In  "the  rough"  means  that  one  surface  is  not  polished  or  finished. 

5 


66 


PRISMS 


grinds  the  second  surface  must  be  in  keeping  with  the 
prismatic  effect  which  the  prescription  calls  for. 

In  place  of  the  above  formula  the  prescriber  could 
have  ordered  +4  sphere  decentered  10  millimeters 
downward  axis  90°.  For  this  prescription  the  optician 
would  take  the  +4  sphere  and  mark  with  a  dot  the 
true  center  (dot  i  in  Fig.  75)  and  also  mark  the  shape 
of  the  lens  he  is  to  cut  out  and  in  place  of  cutting  it  as 


FIG.  74. — Plano-convex  sphere  in  the  rough.     Straight  dotted  line  for  a 
plano-sphero-prism.     Curved  dotted  line  for  meniscus  sphero-prism. 


indicated  by  the  dotted  line,  follows  the  continuous 
line  and  in  this  way  leaves  the  optic  center  10  milli- 
meters downward  or  below  the  geometric  center  at  2. 
In  profile  (Fig.  76)  this  +4  spheric  lens  shows  the 
prism  thus  manufactured  by  decentering. 

The  rule  for  decentering  lenses  to  obtain  a  certain 
amount  of  prismatic  effect  is  as  follows: 

"For  every  centimeter  (10  millimeters)  of  decentering 
there  will  be  produced  as  many  centrads  or  prism- 


COMBINING   A    PRISM    WITH  A    SPHERE 


67 


diopters  as  there  are  diopters  in  the  meridian  which  is 
decentered."  In  the  example  just  given  (+4  sphere 
O  4A  base  downward  axis  90°)  it  must  first  of  all  be 
remembered  that  this  is  a  4  diopter  lens  and  secondly 
if  the  optic  center  is  placed  10  millimeters  away  from 
the  geometric  center  the  effect  will  be  a  +4  sphere  O 
4  prisms;  in  other  words,  as  previously  mentioned,  it 


»  .  c 

FIG.  75.  FTG.  76. 

FIG.  75  — CIRCLE  =  plano-convex  lens  in  the  rough.  I  =  optic  and 
geometric  centers  superimposed.  At  2  the  geometric  center  is  above. 

FIG.  76. — Profile  of  Fig.  75  showing  geometric  center  at  2  and  optic 
center  at  i. 


will  be  +4  sphere  decentered  10  millimeters  downward 
axis  90°  (Figs.  75  and  76).  According  to  the  same  rule  if 
the  +4  sphere  had  been  decentered  5  millimeters  the 
effect  would  have  been  2  prisms,  if  it  had  been  decen- 
tered 21/2  millimeters  the  effect  would  have  been  i 
prism,  if  it  had  been  decentered  15  millimeters  the 


68  PRISMS 

effect  would  have  been  6  prisms.  Likewise  if  the 
denominator  of  the  sphere  had  been  a  minus  in  place 
of  a  plus,  the  effect  would  have  been  the  same,  also 
if  a  plus  or  minus  i,  2,  3,  5,  6,  7,  8,  etc.,  was  decentered 
10  millimeters,  the  prismatic  effect  would  be  i,  2,  3,  5, 
6,  7,  8,  etc.,  centrads  or  prism-diopters  respectively. 
If  the  sphere  is  plus  or  minus  0.25,  0.50  or  0.75  and  is 
decentered  10  millimeters  the  prismatic  effect  is  1/4, 
1/2,  and  3/4  of  a  centrad  or  prism-diopter  respectively. 
Another  rule  for  decentering  is  to  multiply  the  number 
of  prisms  in  the  prescription  by  10  and  divide  the 
amount  by  the  number  of  diopters  in  the  meridian 
which  is  to  be  decentered  and  the  quotient  will  be  the 
number  of  millimeters  for  decentering.  In  the  above 
example,  +4  sphere  O  4A  base  downward  axis  90°, 
the  number  of  prisms  is  4  and  multiplying  4  by  10 
equals  40,  dividing  this  amount  by  4  (the  number  of 
the  diopters  in  the  meridian  of  90°)  and  the  quotient 
is  10  millimeters,  namely  +4  sphere  decentered  10 
millimeters  downward  axis  90°. 

Combining  a  prism  with  a  cylinder  (plus  or  minus) 
requires  extra  consideration,  as  it  depends  in  which 
meridian  the  base-apex  line  of  the  prism  is  to  be  placed 
and  which  meridian  is  to  be  decentered.  The  reader 
must  remember  that  a  cylinder  does  not  refract  rays 
of  light  in  the  meridian  corresponding  to  its  axis.  Fig. 
77  shows  a  +4  cylinder  axis  90°.  Opposite  to  axis 
90°  (that  is  in  the  180  meridian),  the  strength  of 
the  cylinder  is  +4,  but  on  axis  90°  there  is  no  curve 
to  the  glass,  and  there  is  therefore  no  refraction  in  the 
90°  meridian.  Outlining  the  spectacle  lens  on  the 


COMBINING   A    PRISM    WITH  A    SPHERE  69 

surface  of  the  cylinder  as  indicated  by  the  figure  i 
in  Fig.  77,  there  would  not  be  any  prismatic  effect 
produced  if  this  lens  was  thus  cut  out  of  the  cylinder, 
but  if  the  lens  outlined  below  was  cut  out,  then  the 
prismatic  effect  would  be  4  centrads  or  prism-diopters 
because  the  geometric  center  would  then  be  10  milli- 


^-180°  =+4 


FIG.  77. 


meters  to  one  side  of  the  axis.  Namely,  +4  cyl. 
axis  90  o  4A  base  in  axis  180°  is  equal  to  a  +4  cyl. 
axis  90°  decentered  10  millimeters  in,  on  axis  180°. 

From  the  above  statements,  the  following  may  be 
deducted: 

(i)  A  cylinder  per  se  cannot  be  decentered  on  its 
axis. 


70  PRISMS 

(2)  Decentering  a  cylinder  one  centimeter  in  the 
meridian  at  right  angles  to  its  axis  will  produce  the 
effect  of  as  many  prism-diopters  or  centrads  as  there 
are  diopters  in  the  cylinder.  Plus  or  minus  i,  2,  3,  4,  5, 
or  6  cylinder  axis  90°,  decentered  10  millimeters  on 
the  meridian  of  180°  will  give  the  effect  of  i,  2,  3,  4,  5, 
and  6  prism-diopters  or  centrads  respectively.  The 


FIG.  78. — Cylinder  in  the  rough  marked  with  dotted  lines  ready  to  be  ground 
to  get  the  prism  combination. 


same  rule  applies  to  0.25,  0.50  and  0.75  cylinder  axis 
90°.  The  equivalent  of  +4  cyl.  axis  180  o  4A  base 
down  is  a  4A  base  down  axis  90°  with  a  +4  cyl.  axis 
1 80  superimposed  or  as  in  Fig.  78  the  optician  will 
take  a  +4  cyl.  axis  180°  in  the  rough  and  grind  the 
other  surface  plane  (see  dotted  line  same  Fig)  and  at 
an  angle  which  would  produce  the  desired  prismatic 
effect — in  this  instance  4. 


COMBINING  A  PRISM  WITH  A  SPHERE  71 

COMBINING  A  PRISM  WITH  A  PLUS  OR  MINUS  CYLINDER 
WHICH  HAS  ITS  AXIS  OBLIQUELY  PLACED 
TO  THE  BASE-APEX  LINE  OF  THE 
PRISM 

For  instance,  +4  cylinder  axis  45  o  2A  base  in, 
axis  1 80.  This  is  equivalent  to  a  2A  base  in  and  a 
+4  cylinder  axis  45  superimposed  or  the  optician 
takes  the  +4  cylinder  in  the  rough  and  grinds  the 


135 


FIG.  79. — Cylinder  in  the  rough  marked  with  dotted  line  and  an  X  ready 
to  be  cut  thus  producing  a  decentered  cylinder. 

opposite  surface  plane  and  at  an  angle  to  give  the 
desired  prismatic  effect.  In  this  formula  for  the  pur- 
pose of  decentering  it  is  necessary  to  know  the  dioptric 
strength  of  the  +4  cylinder  in  the  180  meridian  when 


72  PRISMS 

the  axis  of  the  cylinder  is  at  45°.  Fig.  79  shows  such 
a  cylinder  with  its  axis  at  45°.  The  meridians  of  90°, 
1 80°  and  135°  are  also  shown.  If  the  spectacle  lens 
indicated  by  the  continuous  line  was  cut  out  of 
the  cylinder  there  would  not  be  any  prismatic  effect 
produced  as  the  geometric  center  and  cylinder  axis 
coincide  and  it  would  simply  be  a  +  4  cyl.  axis 
45°.  But  if  the  spectacle  lens  was  cut  out  as  indi- 


FIG.  80. — Geneva  lens  measure. 

cated  by  the  dotted  line  then  there  would  be  a  2A 
base  in  axis  180  in  combination  with  the  cylinder. 
This  cylinder  was  decentered  10  millimeters*.  The 
method  of  finding  out  the  strength  of  any  cylinder  in 
any  meridian  is  to  apply  the  Geneva  Lens  measure 
(Fig.  80)  to  the  meridian  to  be  decentered. 

In  other  words,  a  +4  cyl.  axis  45°  has  the  strength 


COMBINING   A    PRISM    WITH  A    SPHERE  73 

of  2  diopters  in  the  180  meridian  and  decentering  a  2 
diopter  lens  10  millimeters  gives  the  effect  of  2  prisms. 

COMBINING  A  PRISM  WITH  A  SPHERO-CYLINDER  OF 
SAME  SIGN 

In  the  following  example  +1.00  o  +3.00  cyl. 
axis  90  o  i  A  base  out,  axis  180°.  This  is  equivalent 
to  a  + 1 .00  sphere  on  one  surface  of  the  i  prism  base 
out  axis  180  and  a  +3.00  cyl.  axis  90°  on  the  other 
surface.  Or  if  decentered  all  that  is  necessary  to  re- 
member is  that  in  the  180  meridian  where  the  decen- 
tering is  to  be  done,  there  are  4  diopters,  i  for  the 
sphere  and  3  for  the  cylinder,  and  to  get  the  effect  of 
a  i  prism  in  4  diopters  the  sphere-cylinder  must  be 
decentered  21/2  millimeters;  namely,  +  i.oo  sphere 

0  +3.00  cyl.  axis  90°  decentered    2   1/2  millimeters 
outward,  axis  180°. 

If  this  sphere-cylinder  had  been  decentered  in  the 
same  meridian  5,  7  1/2  or  10  millimeters,  the  prismatic 
effect  would  have  been  2,  3  and  4  prisms  respectively. 
This  applies  of  course  to  the  180  meridian,  but  if  the 
decentering  had  been  done  in  the  vertical  meridian 
then  the  calculations  would  be  entirely  different,  for  it 
will  be  observed  that  in  the  meridian  of  90°  there  is  only 

1  diopter.     If   the   sphero-cylinder   to   be   decentered 
contains  a  plus  sphere  with  a  minus  cylinder,  the  pre- 
scriber  must  remember  that  one  neutralizes  the  other 
to  a  certain  extent  and  he  must  calculate  accordingly, 
for  example,  in   —  i,  sphere   O    +3.00  cyl.  Axis  90° 
O  2V  base  out,  axis  180°,  this  sphero-cylinder  would 


74  PRISMS 

have  to  be  decentered  10  millimeters  as  follows:  —  i 
sphere  O  +  3-  cyl.  axis  90°  decentered  10  millimeters 
outward  axis  180°.  Finally  a  decentered  lens  differs  in 
no  respect  optically  from  a  lens  which  contains  a 
prism. 

If  for  any  reason,  there  is  a  desire  to  order  prisms 
which  will  give  rays  of  light  a  deviation  of  i  degree, 
then  it  will  be  necessary  to  decenter  the  lens  17  1/2 
millimeters  (11/16  of  one  inch)  for  each  degree. 

A  very  important  fact  to  remember  in  the  ordering 
of  lenses  to  be  decentered  is  that  many  lenses  are  not 
of  sufficient  width  or  strength  to  permit  of  decentering, 
especially  if  the  lens  is  weak  and  the  prism  is  strong. 
For  instance  the  following:  +0.50  sph.  O  4V  base  up. 
This  should  be  made  by  taking  a  +0.50  sphere  in  the 
rough  and  cutting  off  the  second  surface  at  the  angle 
which  would  produce  the  4V  base  up  (Fig.  74).  If 
the  prescriber  wrote  this  formula  for  decentering  as 
follows:  +0.50  sph.  decentered  80  millimeters  (8  centi- 
meters) upward  axis  90  he  would  find  that  such  a 
prescription  would  display  great  ignorance  and  invite 
suspicious  criticism  of  the  prescriber's  knowledge. 
Weak  lenses  do  not  come  large  enough  for  any  such 
purpose. 

The  following  tables  by  Dr.  Jackson  and  Dr.  Wallace 
are  self-explanatory: 


COMBINING   A    PRISM    WITH  A    SPHERE 


75 


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To  detect  malingerers  who  profess  monocular 
blindness,  so  as  to  obtain  damages  for  supposed  injuries, 
or  who  wish  to  escape  war  service,  or  those  cases  of 
hysteric  blindness  wishing  to  create  sympathy.  This 
test  or  use  of  a  prism  is  known  as  the  diplopia  test, 
and  is  practised  as  follows:  A  seven  P.  D.,  base  up 
or  down,  and  a  blank  are  placed  in  the  trial-frame 
corresponding  to  the  "blind"  eye;  nothing  is  placed 
in  front  of  the  seeing  eye;  the  trial-frame,  thus  armed 
(without  the  patient  seeing  what  is  being  done),  is 
placed  on  the  patient's  face  and  he  is  instructed  to 
read  the  card  of  test-letters  on  the  wall  across  the  room. 
While  he  is  thus  busy  reading,  and  purposely  contra- 
dicted by  the  surgeon,  so  as  to  get  his  mind  from  his 
condition,  the  surgeon  suddenly  removes  the  blank 
from  the  "blind"  eye.  The  patient  exclaiming  that 
he  sees  two  cards  and  two  of  all  the  letters  proves  the 
deception.  Another  way  to  detect  "deceivers"  is  to 
place  the  trial-frame  on  the  patient's  face  with  a  blank 
on  the  "blind"  eye,  nothing  is  placed  in  front  of  the 
seeing  eye;  the  examiner  then  slowly  passes  a  square 
prism  of  10  or  12  centrads  base  down,  axis  90°  before 
the  seeing  eye  as  the  patient  observes  the  card  of  test 
letters  across  the  room.  As  the  prism  base  bisects 
the  patient's  pupil  horizontally  the  eye  immediately 

78 


USES   OF   PRISMS   IN   OPHTHALMOLOGY 


79 


sees  two  test  cards,  etc.;  then  the  examiner  suddenly 
and  gracefully  removes  the  blank  from  the  "blind" 
eye  with  his  other  hand  and  at  the  same  time  passes 
the  prism  over  the  entire  pupil  of  the  good  eye.  The 
patient,  still  admitting  diplopia,  proves  his  conspicuous 
inexactness  for  veracity.  This  latter  test  does  not 
merit  the  writer's  consideration  as  much  as  the  former 
test,  although  it  is  wrell  to  bear  in  mind  both  of  these 


FIG.  81. — Phorometer.  This  apparatus  contains  two  eye-pieces  for  trial 
lenses;  two  rotary  prisms;  a  Stevens  phorometer;  twoMaddox  multiple  rods 
(one  for  each  eye,  one  at  axis  90,  and  the  other  at  axis  180) ;  also  a  spirit 
level,  etc. 

prism  tests  in  case  the  patient  has  been  previously 
examined  by  either  one  of  them. 

To  ascertain  the  power  of  Adduction  (Prism 
convergence) . 

Abduction  (Prism  divergence)  and  Sursumduc- 
tion. 

In  making  these  tests  the  patient  should  be  comfort- 
ably seated  facing  a  point  of  steady  white  light  on  a 
plane  dark  surface  situated  at  a  distance  of  6  meters ; 
this  light  should  be  on  a  level  with  the  eyes  or  slightly 


80  PRISMS 

below  the  level.  A  suitable  trial-frame  should  rest 
easily  on  the  patient's  nose  and  ears,  although  a  pho- 
ro meter  (Fig.  81)  is  recommended  in  place  of  the  trial- 
frame. 

Adduction. — To  test  adduction,  prisms  with  their 
bases  inward  are  placed  before  one  or  both  eyes  (pref- 
erably before  one  eye).1  Begin  with  a  weak  prism  and 
gradually  increase  the  strength  of  the  prism  until  the 
patient  states  that  he  sees  two  distinct  lights.  For  ex- 
ample, if  with  19  centrads,  base  out  before  the  left  eye, 
two  lights  are  seen  in  the  horizontal  plane  and  with  18 
centrads  only  one  light,  then  18  centrads  represents  the 
maximum  prism  convergence  for  these  eyes. 

Abduction. — This  test  is  pursued  as  in  testing  for 
adduction,  but  the  prism  is  placed  base  inward, 
beginning  with  a  weak  prism  and  gradually  increasing 
the  strength  until  the  patient  states  that  he  sees  two 
distinct  lights.  For  example,  if  with  7  centrads,  base  in, 
before  the  left  eye  two  lights  are  seen  in  the  horizontal 
plane,  and  with  6  centrads  only  one  light,  then  6  cen- 
trads represents  the  maximum  prism  divergence. 

Sursumduction. — This  is  the  power  of  uniting  or 
fusing  the  image  of  the  light  of  one  eye  with  the  image 
of  the  same  light  seen  by  the  other  eye  through  a  prism 
base  up  or  down  axis  90°.  For  example,  if  a  3  1/2 
centrad  prism  is  placed  base  up  axis  90°  before  either 
eye1  and  diplopia  results  and  persists,  and  then  a  3 
centrad  is  substituted  and  there  is  no  diplopia,  then 
the  maximum  amount  of  sursumduction  is  said  to  be 
3  centrads. 

1  The  writer  is  in  the  habit  of  placing  the  prism  before  the  left  eye  in 
making  these  estimates. 


USES    OF    PRISMS    IN    OPHTHALMOLOGY  8 1 

The  writer  strongly  recommends  the  use  of  the 
rotary  prism,  which  will  greatly  facilitate  making  the 
above  tests,  and  those  referred  to  later. 

The  following  nomenclature  of  muscular  anomalies 
suggested  by  Dr.  George  T.  Stevens  of  New  York  is 
in  popular  use : 

Orthophoria  is  perfect  binocular  fixation,  also  spoken 
of  as  equipoise,  binocular  equilibrium  or  parallelism. 
With  a  thorough  understanding  of  the  three  conditions 
just  described  and  which  most  authorities  consider  as 
standard  (adduction  being  three  times  as  great  as  ab- 
duction, and  sursumduction  equalling  2  1/2  or  3  cen- 
trads),  the  reader  may  now  appreciate  any  departure 
from  these  standard  conditions. 

Heterophoria,  imperfect  binocular  balance,  or 
imperfect  binocular  equilibrium. 

Heterotropia,  a  squint  or  decided  deviation  or 
turning  from  parallelism. 

Hyperphoria,  a  tendency  of  one  eye  to  deviate 
upward. 

Hypertropia,  a  deviation  of  one  eye  upward. 

Esophoria,  a  tendency  of  the  visual  axis  to  deviate 
inward. 

Esotropia,  a  deviation  of  the  visual  axis  inward. 

Exophoria,  a  tendency  of  the  visual  axis  to  deviate 
outward. 

Exotropia,  a  deviation  of  the  visual  axis  outward. 

Hyperesophoria,  a  tendency  of  the  visual  axis  of 
one  eye  to  deviate  upward  and  inward. 

Hyperesotropia,  a  deviation  of  the  visual  axis  of 
one  eye  upward  and  inward. 

6 


82  PRISMS 

Hyperexophoria,  a  tendency  of  the  visual  axis 
of  one  eye  upward  and  outward. 

Hyperexotropia,  a  deviation  of  the  visual  axis  of 
one  eye  upward  and  outward. 

As  the  title  of  this  work  does  not  call  for  any  extended 
discussion  on  the  subject  of  the  extra-ocular  muscles, 
the  writer  therefore  limits  himself  to  the  consideration 
of  prisms  as  applied  to  making  tests  for  muscular 
anomalies  or  for  their  treatment.  For  a  full  considera- 
tion of  the  extra-ocular  muscles  the  reader  is  referred  to 
the  author's  work  on  "  Refraction  and  How  to  Refract." 

Tests  for  Heterophoria  and  Heterotropia. — 
There  are  many  of  these  tests  and  each  has  more  or 
less  value.  Like  the  many  tests  for  astigmatism  they 
should  be  understood  and  then  the  reader  may  decide 
for  himself  to  use  one  or  more  of  them  as  they  appeal 
to  his  judgment. 

Von  Graefe  Equilibrium  Test.— Fig.  82,  A.  This 
test  is  a  black  dot  one  inch  in  diameter  at  the  middle  of 
a  straight  line  1 2  inches  long  passing  through  it,  drawn 
on  a  white  card  and  hung  on  the  wall  6  meters  from  the 
patient's  eyes,  the  dot  being  on  a  level  with  the  eyes. 
This  card  should  be  hung  in  a  bright  light  or  illuminated 
by  reflected  light.  As  the  patient  gazes  at  this  dot  and 
line  a  7  centrad  prism  is  placed  base  down  axis  90° 
before  the  left  eye.  This  produces  an  image  of  the  line 
and  dot  upward  which  belongs  to  the  left  eye  (B  in  Fig. 
82),  the  lower  image  belongs  to  the  right  eye.  If  the 
upper  dot  is  directly  above  the  lower  dot  and  the  black 
lines  are  superimposed,  running  through  both  dots  then 
there  is  no  lateral  deviation  (Fig.  82,  B). 


USES    OF    PRISMS    IN    OPHTHALMOLOGY  83 

Esophoria. — If,  however,  the  upper  dot  and  line 
appear  to  the  left  (Fig.  82,  C)  then  there  is  esophoria 
and  the  amount  of  the  esophoria  is  represented  by 
the  strength  of  prism  placed  base  outward  before  the 


FIG.  82. — Von  Graefe  line  and  dot  test.  A  =  Line  and  dot.  B  =  No 
lateral  deviation.  C  =  Esophoria.  D  =  Exophoria.  E  =  No  vertirle 
deviation.  F  =  Left  hyperphoria.  G  =  Right  hyperphoria.  L  =  Image 
of  left  eye.  R  =  Image  of  right  eye. 


right  eye  (or  the  left)  which  will  put  the  upper  dot 
directly  above  the  lower  one  as  Fig.  82,  B. 

Exophoria. — If  the  upper  dot  and  line  appear  to 
the  right  (Fig.  82,  D)  then  there  is  exophoria  and  the 
amount  of  the  exophoria  is  represented  by  the  strength 


84  PRISMS 

of  prism  placed  base  inward  before  the  right  eye1 
(or  the  left)  which  will  put  the  upper  dot  directly 
above  the  lower  one. 

Hyperphoria. — Place  a  10  centrad  prism  base  in 
axis  1 80°  before  the  left  eye,  and  have  the  line  and  dot 
placed  horizontally.  If  the  eyes  see  two  dots  on  one 
line  (Fig.  82,  E)  then  there  is  no  vertical  deviation.  If 
the  right  dot  and  line  appear  higher  than  the  left  line 
and  dot  then  there  is  left  hyperphoria  (Fig.  82,  F).  If 
the  right  dot  and  line  appear  lower  than  the  left  line  and 
dot  then  there  is  right  hyperphoria  (Fig.  82,  G). 

Prism  Tests. — Place  a  7  centrad  prism  in  the  trial- 
frame  or  phorometer  base  down  axis  90°  before  the 
left  eye  as  the  two  eyes  look  at  the  point  of  light  as 
described  under  Adduction.  This  prism  produces  ver- 
tical diplopia.  The  upper  light  naturally  belongs  to 
the  left  eye  under  these  conditions,  and  if  it  is  directly 
above  the  other,  then  there  is  no  lateral  deviation. 

Esophoria. — If  the  upper  light  is  to  the  left  of 
the  lower,  then  the  condition  is  one  of  esophoria  and 
its  amount  is  equal  to  the  strength  of  the  prism  placed 
base  outward  before  the  right  eye  which  will  bring  one 
light  directly  above  the  other. 

Exophoria. — If  the  upper  light  is  to  the  right  of 

1  The  reader's  careful  attention  is  called  to  the  writer's  method  of  making 
the  foregoing  test  as  it  is  similar  to  the  tests  which  are  to  be  described ;  namely, 
that  the  right  eye  is  free  or  unencumbered  to  fix  the  object  or  white  light;  and 
the  right  eye  is  thus  reserved  for  the  use  of  the  correcting  prism.  Furthermore, 
the  amount  of  the  esophoria  is  estimated  by  the  prism  base  out;  exophoria  by 
the  prism  base  in;  left  hyperphoria  by  the  prism  base  up  before  the  right  eye 
and  right  hyperphoria  by  the  prism  base  down  before  the  right  eye.  Finally, 
in  place  of  any  lengthy  description  of  esophoria,  exophoria  and  hyperphoria 
as  each  test  is  described,  the  reader  is  referred  to  the  respective  illustrations. 


USES    OF    PRISMS    IN    OPHTHALMOLOGY  85 

the  lower,  then  the  condition  is  one  of  exophoria  and 
its  amount  is  equal  to  the  strength  of  the  prism  placed 
base  in  before  the  right  eye  which  will  bring  one  light 
directly  above  the  other. 

Hyperphoria. — Place  a  10  centrad  prism  base 
in  axis  180°  before  the  left  eye,  then  the  left  light 
belongs  to  the  left  eye.  If  the  two  lights  then  appear 
in  the  horizontal  meridian  there  is  no  vertical  de- 
viation. If  the  left  light  is  lower  than  the  right  then 
there  is  left  hyperphoria.  If  the  left  light  is  higher 
than  the  right  then  there  is  right  hyperphoria. 

The  amount  of  the  left  hyperphoria  is  represented 
by  the  strength  of  the  prism  placed  base  up  axis  90° 
before  the  right  eye  which  will  bring  these  two  lights 
exactly  horizontal.  The  amount  of  the  right  hyperpho- 
ria is  represented  by  the  strength  of  the  prism  placed 
base  down  axis  90  before  the  right  eye,  which  will 
bring  these  two  lights  exactly  horizontal. 

Use  of  Ruby  Red  Glass  also  Cobalt  Blue  Glass. 
-To  avoid  confusion  on  the  part  of  the  examiner  and 
patient  in  making  these  tests  for  esophoria,  exophoria 
and  hyperphoria,  as  is  the  case  when  both  lights  are 
white,  it  is  decidedly  better  to  use  a  plane  piece  of  ruby 
red  glass  .or  cobalt  blue  glass  with  the  prism  over  the 
left  eye  and  in  this  way  the  lights  seen  by  the  two  eyes 
are  quickly  differentiated. 

In  making  the  above  tests,  the  writer  uses  a  7  centrad 
prism,  made  either  of  cobalt  blue  glass  or  ruby  red 
glass. 

Maddox  Double  Prism  (Fig.  83). — (Obtuse-angled 
prism.)  This  is  two  prisms  of  6  centrads  each  with 


86  PRISMS 

their  bases  united.  Placed  before  the  left  eye  so  that 
the  bases  bisect  the  pupil  horizontally,  the  left  eye 
will  see  two  images,  one  higher  and  one  lower  than  the 
true  light  seen  by  the  right  (fixing)  eye. 

Maddox  double  prism  with  a  piece  of  ruby  red 
glass  or  a  Maddox  Double  Prism  made  of  ruby  red 
glass.  This  is  far  more  attractive  and  avoids  the  con- 
fusion incident  to  having  the  lights  all  of  one  color  seen 
by  both  eyes  (Figs.  84  and  85). 


FlG.  83. — Maddox  double  prism. 

Cobalt  Blue  Glass  with  the  Maddox  double  prism 

or  the  Maddox  Double  Prism  made  of  Cobalt  Blue 
Glass  (Figs.  86  and  87)  gives  the  test  as  shown  in  Fig.  88. 

The  writer  has  been  unable  to  demonstrate  with  his 
own  eyes,  as  some  authorities  have  done,  that  there  is 
any  definite  streak  of  light  connecting  the  two  lights 
produced  by  the  Maddox  Double  Prism  of  colored  or 
colorless  glass. 

Cone  or  Quadrant  or  Quadrilateral  Prism  (Fig. 
90). — This  is  equivalent  to  a  pair  of  Maddox  Double 
Prisms  superimposed,  one  at  axis  90  and  the  other  at 


USES    OF    PRISMS    IN    OPHTHALMOLOGY 


B 


WL 
C 


D 


FIG.  84. — Maddox  double  prism  of  ruby  red  glass.  A  =  Two  images 
produced  by  double  prism.  B  =  No  lateral  deviation.  C  =  Esophoria. 
D  =  Exophoria. 


88 


PRISMS 


E 


R 


FIG.  85. — E  =  No  verticle  deviation.     F  =  Left  hyperphoria.     G  =  Right 
hyperphoria.     L  =  Image  of  left  eye.     R  =  Image  of  right  eye. 


^^^- 


FIG.  86. 


FIG.  87. 


FIG. 


Maddox  double  prism  made  of  cobalt  blue  glass.  FIG.  86  is  profile  of 
Fig.  87.  FIG.  88  is  double  image  produced  by  Maddox  double  prism  of 
cobalt  blue  glass. 


USES    OF    PRISMS    IN    OPHTHALMOLOGY 


B 


FIG.  89. — Quadrilateral  prism  or  cone  in  red  producing  four  red  images 
connected  by  red  streaks.1  E  =  True  light  seen  by  right  eye.  When  E  is 
equidistant  from  ABCD  there  is  no  displacement,  hence  =  Orthophoria. 
When  E  is  in  the  direction  of  i  =  Left  Hyperphoria;  in  the  direction  of  2  = 
Esophoria;  in  the  direction  of  3  =  Exophoria;  in  the  direction  of  4  =  Right 
Hyperphoria;  in  the  direction  of  5  =  Left  Hyperexophoria;  in  the  direction 
of  6  =  Left  Hyperesophoria. 

1  See  footnote  page  84. 


go  PRISMS 

axis  1 80.  Four  images  of  the  light  are  produced  (Fig. 
89),  forming  the  corners  to  a  square  which  are  connected 
by  a  streak  of  light  of  the  color  of  the  glass.  As  this  is 
made  in  colorless  glass,  it  will  be  of  great  advantage  to 
combine  with  it  the  plane  ruby  red  glass  or  have  the 
quadrant  prism  made  of  ruby  red  glass. 

The  Author's  Double  Prism,  Truncated1  (Figs. 
91,   92   and  93). — The  difficulty  experienced  by  the 


FIG.  90. — Cone  or  quadrant  prism. 

writer  in  the  use  of  the  obtuse-angled  prism  in  testing 
for  hyperphoria  of  small  amount  has  been  to  have 
patients  describe  whether  the  central  light  seen  by  the 
right  eye  approached  the  upper  or  lower  images  as  seen 
by  the  left  eye.  To  overcome  this  difficulty  of  decision 
on  the  part  of  the  patient,  the  author  had  the  edge  or 
top  of  the  double  prism  cut  off  evenly  leaving  a  flattened 
top  3  millimeters  wide,  see  Fig.  91,  making  what  he  has 

1  Shown  and  described  to  the  Section  of  Ophthalmology  of  the  College 
of  Physicians  of  Philadelphia,  October  17,  1912. 


FIG.  91. 


FIG.  92. 


FIG.  93. 


Author's  double  prism  of  cobalt  blue  glass.  Fig.  91  is  profile  of  Fig.  92. 
Fig.  93  is  triple  images  connected  by  a  streak  as  seen  through  this  double 
prism. 


Qfir) 

IL      R 


R 


D 


E 


FIG.  94. — Triple  images  and  streak  produced  by  author's  double  prism  in 
cobalt  blue  glass.  B  =  No  lateral  deviation.  C  =  Esophoria.  D  = 
Exophoria.  E  =  Left  Hyperexophoria. 


IWB 


FIG.    95. — F    =    No   verticle   deviation.     G   =   Left  Hyperphoria.     H 
Right  Hyperphoria.     L  =  Image  of  left  eye.     R  =  Image  of  right  eye. 


USES    OF   PRISMS    IN   OPHTHALMOLOGY 


D 

FIG.  96. — Author's  double  prism  of  ruby  red.  A 
nected  by  streak.  B  =  No  lateral  deviation.  C 
Exophoria.  E  =  Left  Hyperexophoria. 


E 

Three  images  con- 
Esophoria.     D   -» 


PRISMS 


G 


H 


FIG.   97. — F    =    No   verticle   deviation.     G   =   Left  Hyperphoria.     H 
Right  Hyperphoria. 


USES    OF    PRISMS    IN   OPHTHALMOLOGY 


93 


chosen  to  call  a  truncated  prism.1  This  is  made  either 
of  ruby  red  glass,  cobalt  blue  glass  or  colorless  glass. 
With  this  form  of  double  prism  placed  before  the  eye  the 
observer  immediately  sees  a  central  true  light,  and  an 
image  above  and  an  image  below,  equidistant  from  it, 
if  the  truncated  prism  has  been  accurately  ground. 
These  three  lights  are  seen  to  be  connected  by  a  band 
of  light,  Fig.  93,  and  the  whole  is  distinctive  from  the 
single  white  light  of  the  right  eye.  For  the  illustrative 
description  of  the  tests  see  Figs.  94,  and  95,  also  96 
and  97. 


FIG.  98. — Maddox  rod. 


FIG.  99. 


Maddox  Rod.— This  is  a  single  glass  rod  or  a  series 
of  glass  rods  of  red  or  colorless  glass  (Figs.  98  and  99) 
placed  in  a  metal  cell  of  the  trial  case,  and  the  eye 
looking  through  it  at  the  light,  will  see  the  image  of  the 
light  distorted  into  a  streak  of  broken  light.  A  strong 
+  cylinder  from  the  trial  case  may  be  used  for  the  same 
purpose.  As  the  rod  refracts  rays  of  light  opposite  to 
its  axis,  the  eye  will  see  a  streak  of  light  in  the  reverse 

1  "  A  cone  or  pyramid  whose  vertex  is  cut  off  parallel  to  the  base  by  a 
plane." 


94 


PRISMS 


B 


E 


FIG.  too. — A  =  Image  of  Maddox  single  rod  in  red.  B  =  No  lateral 
deviation.  C  =  Esophoria.  D  =  Exophoria.  E  =  Left  Hyperexophoria. 
R  =  Image  of  right  eye.  L  =  Image  of  left  eye. 


USES    OF    PRISMS    IN    OPHTHALMOLOGY 


95 


J 

^R 

L 

G 

@R 

T 

• 

L 

©R 

FIG.  ioi. — F*=  No  verticle  deviation.     G  =  Left  Hyperphoria.     H  =  Righ 
Hyperphoria,    L  =  Image  of  left  eye.    R  =  Image  of  right  eye. 


96 


PRISMS 


'R 


C 

FIG.  102. — A  =  Double  images  produced  by  Maddox  double  prism  in  red 
with  Maddox  rod.  B  =  No  lateral  deviation.  C  =  Esophoria.  D  = 
Exophoria. 


USES    OF    PRISMS   IN   OPHTHALMOLOGY 


97 


E 


R 


)R 


FIG.   103.— E    =   No  verticle  deviation.    F    =   Left  Hyperphoria      G 
Right  Hyperphoria.     R  =  Image  of  right  eye. 


98  PRISMS 

meridian  to  that  in  which  the  axis  is  placed.  See  Figs. 
98  and  99,  also  Figs.  100  and  101. 

Maddox  Double  Prism  and  Rod  Combined. — This 
produces  two  streaks  of  light  (Fig.  102,  A)  white  or  red 
as  the  operator  may  choose.  See  illustrations  in  Figs. 
101,  102  and  103.  This  combination  like  the  double 
prism  by  itself  is  not  as  satisfactory  a  test  for  esophoria 
or  exophoria  as  it  is  for  hyperphoria.  In  the  former 
condition  the  right  eye  will  frequently  fuse  its  image 
with  one  of  the  light  streaks  of  the  left  eye,  i.e.,  with 
the  right  one  in  esophoria  and  the  left  one  in  exophoria 
(Fig.  102,  C  and  D). 

Convex  Spherical. — Using  a  +15  diopter  sphere 
before  the  left  eye  a  very  much  blurred  image  is  seen 
by  this  eye,  and  the  position  of  the  image  of  the  right 
eye  relative  to  this  blurred  image  gives  the  diagnosis 
of  the  muscular  inbalance.  If  the  image  of  the  right 
eye  centers  on  the  blurred  image  then  the  condition 
is  one  of  orthophoria ;  if  to  the  right  or  left  or  above  or 
below  the  blurred  image,  then  it  will  be  esophoria, 
exophoria,  right  hyperphoria  or  left  hyperphoria  re- 
spectively. However,  the  writer  is  not  partial  to  this 
test,  as  it  is  most  difficult  for  the  average  patient  to 
maintain  exact  fixation  with  his  left  eye. 

Tangent  Scale  and  Maddox  Rod. — This  tangent 
scale1  of  Prentice  (Fig.  57)  with  a  central  light  as  a 
fixing  object  and  a  Maddox  rod  before  the  left  eye 
furnishes  an  ideal  test  as  the  record  of  the  amount 
of  the  deviation  can  be  stated  by  the  patient. 
Each  line  of  displacement  of  the  streak  is  equivalent 

1  Archives  of  Ophthalmology,  Vol.  XIX,  No.  i,  pages  64  and  68. 


USES   OF   PRISMS    IN    OPHTHALMOLOGY  99 

to  one  centrad  or  prism-diopter.  For  example,  if  the 
patient  states  that  the  streak  is  situated  vertically  on 
the  zero  line  there  is  no  lateral  deviation,  if  the  streak 
is  situated  horizontally  on  the  zero  line  there  is  no 
vertical  deviation ;  if  the  streak  is  to  the  left  or  right  or 
above  or  below  the  zero  line  then  esophoria,  exophoria, 
and  right  or  left  hyperphoria  are  present  and  to  the 
amount  as  indicated  by  the  position  of  the  streak  whether 
on  line  numbered  i,  2,  3,  etc.  If  the  streak  is  between 
two  lines  then  there  is  also  a  fraction  of  a  centrad  or 
prism-diopter  of  deviation. 

Another  way  to  use  the  tangent  squares  (Fig.  57) 
is  to  place  a  7  centrad  prism  base  down  axis  90°  before 
the  left  eye  and  in  this  way  produce  an  upper  image 
of  the  chart.  If  the  upper  image  is  displaced  directly 
upward  with  the  vertically  numbered  lines  coinciding 
then  there  is  no  lateral  deviation.  If  the  upper  image 
appears  to  the  left  the  amount  of  the  esophoria  is 
quickly  diagnosed  and  likewise  the  amount  of  exophoria 
if  the  upper  image  is  to  the  right.  A  10  centrad  prism 
base  in  axis  180  before  the  left  eye  would  diagnose 
the  presence  of  left  or  right  hyperphoria  and  also  the 
amount  of  each. 

Cyclophoria. — (Insufficiency  of  the  oblique  mus- 
cles.) This  test  is  usually  made  at  thirteen  or  eighteen 
inches  from  the  patient's  eyes.  A  narrow  straight  black 
line  is  placed  horizontally  on  a  white  card,  as  the  fixing 
object  at  the  distance  indicated.  A  Maddox  Double 
Prism  is  placed  before  the  left  eye  so  that  the  bases  bisect 
the  pupil  horizontally  and  this  eye  then  sees  two  parallel 
horizontal  lines  if  its  oblique  muscles  are  in  a  standard 


IOO 


PRISMS 


condition.  The  right  eye  sees  but  one  line  between 
the  two  lines  seen  by  the  left  eye.  The  right  eye  is  the 
one  being  tested  and  the  position  of  the  middle  line 
furnishes  the  diagnosis.  If  the  left  eye  is  to  be  tested 
then  the  Maddox  Double  Prism  must  be  placed  before 
the  right  eye  (Fig.  104). 


FIG.  104. — Tests  for  insufficiency  of  the  oblique  muscles,  i  =  Ortho- 
phoria  or  equilibrium  of  the  obliques.  2  =  Insufficiency  of  left  superior 
oblique.  3  =  Insufficiency  of  right  superior  oblique.  4  =  Insufficiency  of 
the  left  inferior  oblique.  5  =  Insufficiency  of  the  right  inferior  oblique. 


Cyclophoria  and  its  varieties  may  also  be  diagnosed 
by  using  two  Maddox  rods ;  one  at  axis  90°  before  one 
eye  and  the  other  at  axis  180°  before  the  other  eye  and 
a  point  of  light  as  the  fixing  object  at  6  meters.  If 
orthophoria  is  present  the  two  streaks  produced  by  the 
two  rods  will  naturally  form  a  cross;  but  if  cyclophoria 
is  present,  then  one  of  the  streaks  will  show  a  tilting 
or  inclination  from  an  otherwise  true  position  of  being 


USES    OF    PRISMS    IN    OPHTHALMOLOGY  IOI 

horizontal  or  vertical;  indicating  at  once  therefore 
which  eye  is  at  fault  or  has  the  oblique  insufficiency. 
Whenever  the  writer  is  suspicious  of  the  existence  of 
cyclophoria,  he  is  partial  to  the  use  of  a  colorless  rod 
before  one  eye  and  a  red  rod  before  the  other  eye,  but 
each  must  be  placed  with  its  axis  exactly  horizontal. 
If  the  two  streaks  appear  parallel  or  are  superimposed, 
there  is  no  oblique  insufficiency,  but  if  one  streak  dips, 
so  to  speak,  then  cyclophoria  is  present  and  corresponds 
to  the  eye  having  the  corresponding  rod;  the  inclina- 
tion or  dip  furnishing  a  prompt  diagnosis  of  the  muscle 
at  fault.  In  making  either  of  these  tests  extreme  care 
must  be  exercised  to  see  that  the  phorometer  or  trial- 
frame  and  patient's  eyes  are  true  to  the  horizontal 
meridian.  Hyperesophoria  and  Hyperexophoria 
may  be  diagnosed  by  any  of  these  tests  and  are 
easily  recognized  as  shown  in  the  tests  figured  in  89 
and  94. 

While  the  foregoing  tests  are  used  for  heterophoria  or 
latent  squint,  yet  they  are  also  used  for  testing  hetero- 
tropia  or  manifest  squint.  It  is  not  necessary  there- 
fore to  describe  the  tests  for  heterotropia  except  to 
say  that  when  heterotropia  is  of  very  high  degree  and 
one  eye  has  defective  sight,  it  may  be  necessary  to 
begin  the  test  with  a  red  glass  and  strong  prism  before 
the  poor  seeing  eye  so  as  to  engage  its  attention. 

Other  tests  for  heterophoria  and  heterotropia  are 
made  with  the  use  of  apparatus  and  the  following 
have  been  selected  from  several  as  most  worthy  of 
consideration. 

Steven's     Phorometer    (see    Fig.    81). — This    is 


102  PRISMS 


composed  of  two  5  centrad  prisms  each  mounted  in 
a  separate  large  cell  with  cogged  edges;  one  prism  is 
mounted  before  each  eye  and  these  are  connected  by 
a  small  cogged  wheel.  A  convenient  handle  on  the 
right  cell  when  pushed  to  either  side  makes  both  prisms 
revolve  at  the  same  rate  of  speed.  The  marking  on 
the  cell  to  which  the  prism  pointer  is  directed  indi- 
cates the  degree  and  variety  of  heterophoria.  The 
reader  will  appreciate  the  fact  that  this  apparatus  is 
ideal,  but  its  usefulness  is  limited  to  errors  of  10  cen- 
trads.  If  the  operator  wishes  to  use  the  Steven's 
phorometer  to  test  errors  higher  than  10  centrads  he 
must  place  an  additional  prism  from  the  trial-case  next 
to  one  of  the  patient's  eyes.  To  avoid  confusion  it 
might  be  well  to  state  that  these  two  prisms  of  the 
Steven's  phorometer  never  occupy  the  same  position  at 
the  same  time.  They  may  both  be  base  in  or  both  base 
out,  or  one  base  up  while  the  other  is  base  down.  They 
never  reach  a  point  where  one  is  base  in  and  the  other 
base  out,  or  both  bases  down  or  both  bases  up  at  the 
same  time. 

The  apparatus  is  used  as  both  eyes  are  looking  at  the 
point  of  light. 

Dr.  E.  A.  Prince's  Phorometer  (Fig.  105).— This 
instrument  with  its  convenient  handle  is  for  the  patient 
to  hold  before  either  eye  as  directed.  A  4  centrad 
prism  and  a  maddox  rod  are  enclosed  in  a  metal  case. 
A  milled  head  screw  on  one  side  permits  the  patient 
or  operator  to  revolve  the  prism.  The  patient  is  told 
to  fix  with  both  eyes  on  a  point  of  light  at  6  meters. 
If  the  streak  is  vertical  and  to  one  side  of  the  light,  the 


USES    OF    PRISMS   IN    OPHTHALMOLOGY  103 

prism  is  revolved  until  the  streak  and  light  appear  to 
unite.  The  scale  records  the  amount  and  character 
of  the  lateral  deviation.  To  test  hyperphoria,  the 
apparatus  must  be  taken  off  of  the  handle  and  replaced 
with  the  rod  vertical  so  as  to  produce  a  horizontal 
streak  and  then  revolve  the  prism  until  the  streak  and 


FIG.  105. 

light  appear  to  unite.  Unfortunately  this  apparatus 
is  limited  in  its  usefulness  to  4  centrads.  The  Prince 
phorometer  is  admirable,  however,  for  testing  the  in- 
sufficiency of  some  private  patients  away  from  the 
office. 

TheMeister  Phorometer  (Fig.  106). — This  appara- 
tus, with  its  folding  handle,  spirit  level  and  adjustable 
pair  of  15  centrad  prisms  and  adjustable  Maddox 
multiple  red  rod  is  a  veritable  "Multum  inParvo". 
The  writer  takes  great  pleasure  in  giving  it  his  cordial 
endorsement,  for  with  its  strong  prisms  it  will  do  as 
much  and  more  than  the  Stevens  and  Prince  Phoro- 
meters  combined. 


104 


PRISMS 


FIG.  106. — Meister's  Phorometer. 


FIG.  107. — Savage's  cyclophorometer. 


USES  OF  PRISMS  IN  OPHTHALMOLOGY       105 

Savage's  Cyclophorometer  (Fig.  107). — This  in- 
strument is  used  for  detecting  and  measuring  cyclo- 
phoria — a  tendency  of  the  vertical  axes  of  the  eyes  to 
lose  parallelism  with  the  median  plane  of  the  head. 

The  instrument  consists  of  the  equivalent  of  a  two- 
cell  trial-frame,  with  revolving  cells  mounted  so  the 
pupillary  distance  may  be  varied  by  a  set  screw  at  the 
end  of  the  supporting  bar.  The  arm  carrying  the  cells 
is  provided  with  a  leveling  attachment  and  a  spirit 
level. 

In  examining  for  cyclophoria  a  multiple  Maddox  rod 
is  placed  in  each  of  the  revolving  cells  and  a  5 -degree 
prism,  base  up,  behind  one  of  them.  The  patient  sees 
two  horizontal  lines  of  light,  which  should  be  parallel 
and  the  ends  even.  The  latter  can  be  regulated  by 
varying  the  pupillary  distance.  If  the  lines  are  not 
parallel  they  may  be  made  so  by  rotating  either  Maddox 
rod,  the  kind  (plus  and  minus)  and  degree  of  the  error 
being  shown  on  the  scale. 

Cyclo-duction,  the  intrinsic  power  of  each  oblique 
muscle  or  of  both  superior  or  of  both  inferior  obliques 
may  also  be  measured. 

Savage's  Monocular  Phorometer  (Fig.  108).— 
This  instrument  is  designed  for  the  determination  and 
measurement  of  insufficiencies  of  the  various  ocular 
muscles  and  is  based  on  the  principle  that  the  image  in 
one  eye  throughout  every  test  shall  be  undisturbed. 

It  consists  principally  of  a  rotary  variable  prism 
correctly  marked  in  degrees  and  lettered  to  show  the 
various  conditions  of  muscular  imbalance,  such  as 
exophoria,  esophoria,  hyperphoria,  etc.  On  each  side 


106  PRISMS 

of  the  rotary  prism  are  cells,  in  one  of  which,  toward  the 
patient's  face,  is  to  be  placed  the  displacing  prism  for 
causing  diplopia.  These  prisms  are  carefully  mounted 
in  square  cells  for  securing  accurate  position  at  either 
90  degrees  or  180  degrees.  The  instrument  is  supplied 
with  a  spirit-level  and  a  leveling-screw. 


FIG.  108. — Savage's  monocular  phorometer. 

The  prism  is  reversible  for  either  eye. 

While  most  of  the  apparatus  and  descriptions  just 
mentioned  are  for  testing  the  muscular  conditions  at 
6  meters,  it  is  necessary  to  test  muscular  anomalies  at  a 
close  range,  i.e.,  at  13  inches  (33  centimeters)  as  this  is 


USES    OF    PRISMS   IN   OPHTHALMOLOGY 


107 


the  average  reading  and  working  distance  with  the  eyes 
at  close  occupations. 

Convergence. — Con,  "together,"  and  vergere,  "to 
turn";  literally  turning  together.  Standard  eyes,  when 
looking  at  an  object  at  a  distance  of  six  meters  or  more, 
are  not  supposed  to  converge,  the  visual  lines  are  spoken 
of  as  parallel  and  the  power  of  convergence  in  a  state 
of  repose.  The  angle  which  the  visual  line  makes  in 
turning  from  infinity  ( oo.)  or  six  meters  to  a  near  point 
is  called  the  angle  of  convergence,  and  the  angle  which 


FIG.  109. 

is  formed  at  one  meter  distance  by  the  visual  axis  with 
the  median  line  is  called  the  meter  angle,  or  the  unit  of 
the  angle  of  convergence.  (See  I  in  Fig.  109.) 

If  the  visual  line  meets  the  median  plane  at  1/2  meter, 
it  has  then  two  meter  angles  of  convergence;  at  1/4 
meter,  four  meter  angles  of  convergence,  etc.,  or  five 
meter  angles  means  that  the  eye  is  converging  to  a  point 
1/5  meter  distant.  The  size  of  the  meter  angle  varies; 
it  is  not  the  same  in  all  individuals;  in  fact,  the  meter 
angle  is  smaller  in  children  than  in  adults,  as  a  rule,  on 
account  of  the  shorter  interpupillary  distance.  In  chil- 


108  PRISMS 

dren  this  distance  is  about  50  mm.,  whereas  in  adults 
it  is,  on  the  average,  60  or  64  mm. 

If  the  average  distance  between  pupils  in  the  adult  is 
64  millimeters,  then  one  meter  angle  equals  a  deviation 
for  one  eye  of  32  millimeters.  As  the  eyes  converge 
closer  than  one  meter,  the  meter  angle  increases  corre- 
spondingly, the  number  of  meter  angles  is,  therefore, 
the  inverse  of  the  distance  expressed  in  meters.  As  one 
meter  angle  equals  a  deviation  of  32  millimeters,  this 
equals  or  is  equivalent  to  3.2  centrads.  One  centrad 
deviates  a  ray  of  light  .57295°  and  3.2  centrads  would 
therefore  equal  a  deviation  of  i°  50'.  Knowing  the 
prismatic  effect  or  equivalent  of  converging  to  a  point 
at  i  meter,  then  at  3  meter  angles  the  effect  would  be 
three  times  as  great  or  9.6  centrads  or  5°  30'. 

The  reverse  of  this  is  equivalent  therefore  to  placing 
a  9.6  centrads  base  in  axis  180°  before  each  eye  and  the 
eyes  would  see  an  object  at  33  centimeters  as  if  it  were 
located  at  infinity.  In  other  words  when  a  pair  of 
standard  eyes  with  standard  muscles  turn  from  looking 
at  a  distance  of  6  meters  to  fix  on  an  object  at  33  cen- 
timeters, these  eyes  have  developed  a  power  of  conver- 
gence equivalent  to  19  or  20  centrads. 

Any  departure  from  this  standard  unit  of  convergence 
produces  muscular  inbalance  of  the  varieties  already 
described.  / 

Tests  for  Muscular  Inbalance  at  33  Centimeters. 
—Have  the  patient  look  at  a  small  black  dot  with  a  fine 
black  line  2  or  3  inches  long  running  perpendicularly 
through  it,  at  a  distance  of  about  13  inches.  This  is 
known  as  the  line-and-dot  test  of  von  Graefe  for  near 


USES    OF    PRISMS    IN    OPHTHALMOLOGY  IOQ 

testing,  and  on  a  larger  scale  is  described  in  the  previous 
tests  at  6  meters.  A  prism  of  seven  or  eight  centrads 
is  placed,  with  its  base  down,  in  front  of  the  left  eye. 
If  the  patient  sees  two  dots  exactly  one  above  the  other 
on  one  line  there  is  not  supposed  to  be  any  lateral  in- 
sufficiency. If,  however,  there  are  two  lines  and  two 
dots,  and  the  upper  dot  and  line  is  on  the  left  then  there 
is  esophoria  for  near.  The  amount  of  the  esophoria 
is  represented  by  the  strength  of  the  prism,  placed  base 
outward  before  the  right  eye,  which  will  bring  the  two 
dots  exactly  on  one  line.  If  the  upper  dot  and  line  are 
to  the  right,  then  there  is  exophoria  for  near,  and  the 
amount  of  the  exophoria  is  represented  by  the  strength 
of  the  prism  placed  base  inward  over  the  right  eye 
which  will  bring  the  twro  dots,  one  above  the  other,  on 
one  line. 

Another  method  for  testing  lateral  insufficiency  at 
the  reading  distance  of  13  inches  is  to  have  a  card  about 
6  inches  square,  and  on  this  card  to  draw  a  heavy  black 
line  about  3  inches  long;  this  line  to  be  placed  exactly 
horizontal.  At  the  middle  of  the  horizontal  line  draw 
a  heavy  black  line,  1/2  inch  long,  extending  vertically 
from  the  horizontal  line;  this  short  vertical  line  to  be 
capped  with  an  arrow  point.  The  horizontal  line  is 
divided  off  into  equal  spaces,  each  31/3  millimeters 
apart  and  numbered  from  i  to  15  each  side  of  the  arrow; 
those  to  the  left  of  the  arrow  are  marked  "  esophoria," 
and  those  to  the  right  of  the  arrow  are  marked  "  exo- 
phoria" (Fig.  no). 

To  use  this  method,  a  prism  of  8  centrads  is  placed 
base  down  before  the  left  eye;  this  doubles  the  scale 


no 


PRISMS 


vertically;  the  upper  scale  belongs  to  the  left  eye.  The 
number  and  the  word  in  the  upper  scale  to  which  the 
arrow  in  the  lower  scale  points,  is  the  approximation  in 
centrads  of  the  amount  of  the  esophoria  or  exophoria. 
For  instance,  if  the  lower  arrow  points  to  figure  9  in 
the  upper  scale  to  the  right  of  the  upper  arrow,  that  is  to 
the  word  "exophoria,"  then  there  will  be  approximately 
9  centrads  of  "exophoria"  at  this  distance  of  13  inches, 
the  distance  at  which  this  scale  is  intended  to  be  used. 


Esophoria 


15  14  13   12    H   10    9     8     76     54     32     1 


Exophoria 


1     2     3     4     5     0     7     8     9     10    11    12    13    14  15 


FIG.  no. — Scale  for  testing  lateral  insufficiency  at  13  inches. 

To  Test  for  Hyperphoria  at  33  Centimeters.— 

Place  a  10  centrad  prism  base  in  before  the  left  eye  as 
the  right  eye  fixes  the  line  and  dot  of  von  Graefe  as  in 
the  former  test,  except  that  the  line  is  placed  horizon- 
tally. If  there  are  two  dots  on  the  horizontal  line,  then 
there  is  no  vertical  deviation,  but  if  there  are  two  dots 
and  two  lines  one  above  the  other  then  there  is  a  vertical 
deviation.  If  a  prism  base  down  before  the  right  eye 
brings  the  two  lines  together,  then  there  is  right  hyper- 
phoria;  if  the  prism  base  up  before  the  right  eye  brings 
the  two  lines  together,  then  there  is  left  hyperphoria. 

The  large  black  square  and  small  white  millimeter 
square  in  its  center  as  suggested  by  Dr.  Jackson  makes 
an  excellent  test  for  muscular  imbalance  at  33  centimeters 
(Fig.  in).  The  small  white  square  is  made  to  appear 
double  with  a  10  centrad  prism  base  down  before  the 
left  eye. 


USES   OF   PRISMS   IN   OPHTHALMOLOGY  III 

The  small  Greek  cross  (Fig.  112)  suggested  by  Dr. 
S.  L.  Ziegler  answers  the  same  purpose  as  the  Jackson 


FIG.  in. — Dr.  E.  Jackson's  test  for  muscular  insufficiencies  at  33  centimeters. 


FIG.  112. — Dr.  S.  L.  Ziegler's  Greek  cross  as  a  near  test  object. 


squares.     Other  authorities  are  parital  to  a  printed 
word  like  DIOPTER,  for  instance;  this  is  made  to 


112 


PRISMS 


appear  double  with  a  10  centrad  prism  base  down  before 
the  left  eye.  If  the  letteis  appear  directly  above  each 
other,  D  over  D,  I  over  I,  etc.,  then  there  is  no  lateral 
deviation,  etc. 


FIG.  113. — Place  a  10  centrad  prism  base  down  before  left  eye,  if  upper 
cross  appears  to  the  left,  the  condition  is  esophoria;  if  to  the  right,  the  con- 
dition is  exophoria.  Next  place  a  10  or  12  centrad  base  in  over  left  eye,  if 
the  left  cross  is  below,  then  there  is  left  hyperphoria,  if  above,  then  there 
is  right  hyperphoria. 

The  writer,  however,  is  partial  to  the  Maddox  Scale 
shown  in  Fig.  no.  The  Narrow  Lined  Cross  with 
central  dot  is  also  popular  and  is  not  without  merit 
(Fig-  113)- 


CHAPTER  VIII 

PRISM  TREATMENT  FOR  HETEROPHORIA  AND 
HETEROTROPIA1 

As  ametropia  is  the  most  common  cause  of  insuffi- 
ciency (and  of  squint),  the  first  consideration  must  be  to 
select  the  proper  correcting  glasses.  After  this  has  been 
accomplished,  if  the  insufficiency  still  persists  and  the 
patient  is  not  comfortable,  then  the  muscular  imbalance 
should  receive  careful  attention,  and  the  condition  of 
insufficiency  be  studied  from  every  point  of  view. 

The  prescribing  of  prisms,  as  a  fixed  rule,  for  per- 
manent use,  which  neutralize  an  insufficiency,  except 
in  vertical  errors,  or  for  old  people  (see  Exophoria)  is 
often  a  serious  mistake,  as  in  most  instances  prisms 
often  do  more  harm  than  good  by  increasing  instead  of 
diminishing  the  insufficiency. 

Remarks. — Patients  with  heterophoria  cannot  all  be 
prescribed  for  alike  with  the  expectation  of  equally 
good  results  in  every  instance  and  the  writer  from  per- 
sonal experience  divides  these  cases  into  two  classes : 

Class  i  embraces  those  who  are  not  presbyopic  and 
can  use  one  pair  of  glasses  for  all  purposes  of  distant  and 
near  vision. 

1  As  the  treatment  of  the  extra-ocular  muscles  other  than  by  prisms  has 
been  fully  explained  in  the  Author's  work,  "Refraction  and  How  to  Re- 
fract," the  reader  is  referred  to  that  volume. 
8  II 


PRISMS 


Class  2  embraces  those  who  are  presbyopic  or  those 
who  require  two  corrections,  one  for  distant  vision  and 
another  for  near  work,  or  bifocals. 

Exophoria. — (Fig.  114).  Because  the  tests  for 
heterophoria  at  6  meters  show  an  ability  on  the  part  of 
the  patient  to  maintain  equilibrium,  it  must  not  be 
supposed  that  there  may  not  be  a  latent  insufficiency. 


FIG.  114. — Tendency  of  visual  axes  outward. 

The  normal  ratio  of  adduction  to  abduction  (three  to 
one)  should  be  taken  into  consideration  in  every  instance 
before  coming  to  any  definite  conclusion. 

After  the  proper  correcting  glasses  have  been  pre- 
scribed and  the  patient's  general  health  looked  after, 
attention  if  necessary,  should  be  directed  to  strengthen- 
ing the  weak  innervation  and  to  do  this  a  certain  amount 
of  systematic  exercise  known  as  ocular  gymnastics 


HETEROPHORIA  AND  HETEROTROPIA        11$ 

must  be  employed.  That  success  may  result  from 
ocular  gymnastics  means  perseverance  on  the  part  of  the 
patient  and  the  exercises  systematically  executed. 
There  are  two  methods  of  procedure  to  strengthen 
innervation  in  cases  of  exophoria : 

Adduction  Exercise. — i.  Have  the  patient  "fix" 
with  both  eyes  the  point  of  a  pencil,  or  the  end  of  his 
finger  held  at  arm's  length  and  slowly  draw  it  to  a 
point  5  or  3  inches  from  the  bridge  of  his  nose.  If 
diplopia  results  while  doing  this,  the  exercise  should 
cease,  and  be  repeated  at  once  from  the  original  dis- 
tance. This  is  a  very  convenient  exercise  and  should  be 
practised  for  five  or  ten  minutes  after  meals;  never  be- 
fore a  meal,  as  some  patients  become  nauseated  if  the 
stomach  is  empty.  This  mode  of  exercise  to  developed 
adduction,  while  equivalent  to  the  use  of  prisms,  is 
much  better  in  every  way  than  by  prism  exercises ;  in 
fact,  the  writer  has  long  since  abandoned  exercises  with 
prisms  for  cases  of  exophoria. 

Prism  Exercise. — 2.  The  patient  is  placed,  standing, 
about  a  foot  or  two  from  a  point  of  steady  light,  on  a 
level  or  slightly  below  the  level  of  the  eyes,  and  told  to 
look  at  it  and  at  nothing  else.  In  this  position  a  pair  of 
weak  prisms  (2  or  3  centrads),  bases  out,  in  the  trial- 
frame  are  placed  in  front  of  his  eyes. 

Then  he  is  told  to  walk  slowly  backward^across  the 
room,  as  he  keeps  his  eyes  fixed  on  the  point  of  light. 
Should  diplopia  develop  at  any  distance  short  of  20  feet, 
then  he  is  to  raise  the  prisms,  go  back  to  his  original 
position,  and  start  over  again.  Repeating  this  a  num- 
ber of  times  in  the  surgeon's  office,  it  will  be  found  in 


Il6  PRISMS 

most  instances,  that  at  this  first  practice  a  pair  of  5  or 
10  centrads  can  be  overcome  at  a  distance  of  20  feet. 
When  the  distance  of  20  feet  from  the  light  is  reached 
without  developing  diplopia,  the  patient  is  instructed 
to  slowly  count  20  or  30  (keeping  the  light  single  during 
this  time  by  careful  fixation),  then  raise  the  prisms 
(gazing  at  the  light),  and  slowly  count  20  or  30  again. 
This  exercise  is  repeated  three  times  a  day  after  meals 
and  a  number  of  times  at  each  practice.  A  prescrip- 
tion is  then  given  for  such  a  pair  of  square  prisms 
with  a  convenient  frame  to  wear  over  the  patient's 
glasses,  and  with  these  the  patient  continues  the  exer- 
cises at  home.  These  exercises  should,  as  a  rule,  be 
conducted  with  the  patient  wearing  his  correction. 
Instead  of  the  prism-frame  the  patient  may  hold  the 
square  prisms  with  his  hands ;  but  these  are  tiresome  to 
hold,  and  for  general  use  the  prism-frame,  if  not  too 
heavy,  is  preferable.  After  a  few  days  practice  at 
home,  the  patient  returns,  and  stronger  prisms  which 
will  permit  the  patient  to  maintain  single  vision  are 
again  ordered.  This  practice  with  stronger  and 
stronger  prisms  is  renewed  weekly  or  bimonthly 
until  the  patient  is  able  to  overcome  prisms  greatly 
in  excess  of  the  normal  ratio  of  adduction  to  abduction. 
It  is  often  well  to  develop  the  innervation  power  of 
adduction  to  three  or  four  times  the  strength  of  abduc- 
tion; for  when  the  exercises  are  stopped,  some  of  the 
adduction  power  will  rapidly  disappear. 

It  has  been  incidentally  mentioned  that  prisms  should 
not  be  prescribed  in  combination  with  the  ametropic 
correction  for  the  treatment  of  insufficiency,  and  yet 


HETEROPHORIA    AND   HETEROTROPIA  117 

there  is  an  occasional  exception  to  this  statement  for 
patients  who  must  have  prompt,  though  temporary, 
relief.  When  ordering  prisms  as  a  temporary  expe- 
dient, it  is  best  to  prescribe  them  in  the  form  of  "  hook 
fronts,"  so  that  they  may  be  thrown  aside  at  any  time. 
What  has  just  been  stated  in  regard  to  treatment  exer- 
cises applies  particularly  to  patients  in  Class  i. 

Treatment  of  Class  2. — Patients  in  this  class,  as 
just  stated,  are  usually  presbyopic  and  therefore  re- 
quire two  corrections.  Presbyopes  with  exophoria  have 
reached  a  stage  in  life  when  it  is  difficult  or  almost  im- 
possible to  put  new  life  into  old  structures,  and  it  does 
seem  as  if  the  extra-ocular  muscles  like  the  ciliary 
muscle  were  no  exception  to  this  statement;  and  this 
fact  becomes  more  and  more  evident  as  the  patient  passes 
beyond  fifty  years  of  age.  Developing  adducting  power 
by  practising  fixation  at  33  centimeters  may  accomplish 
a  great  deal  of  good  in  some  young  presbyopes,  but 
taking  a  presbyope  of  fifty  or  fifty-five  or  sixty  years  of 
age  and  trying  to  develop  adduction  with  fixation  or 
prism  exercise  is,  in  almost  every  instance  and  with  few 
exceptions,  a  waste  of  time  and  patience.  Presbyopes 
do  not  take  kindly  to  such  treatment  and,  in  the  writer's 
experience,  patients  so  treated  soon  seek  assistance 
elsewhere. 

In  hyperphoria  the  full  prismatic  correction  (except 
in  cases  of  presbyopia)  is  seldom  ordered,  only  about 
two-thirds  or  three-fourths  of  the  amount  is  pre- 
scribed and,  if  of  high  degree,  this  amount  is  usually 
divided  between  the  two  eyes,  base  down  before  one, 
and  base  up  before  the  other. 


Il8  PRISMS 

Testing  the  muscular  condition  at  33  centimeters 
with  the  presbyopic  near  correction  before  the  patient's 
eyes,  there  should  be  about  ten1  centrads  of  exophoria 
normally  at  this  distance,  but  if  there  happens  to  be 
12,  14  or  1 6  centrads  of  exophoria  then  the  presbyope 
is  uncomfortable  and  complains  correspondingly  when 
using  the  eyes  at  near  work  for  any  length  of  time.  The 
prism  treatment  for  exophoria  at  the  working  distance 
in  presbyopes  is  to  add  or  prescribe  prisms  bases  in 
to  be  made  in  the  near  correction.  The  amount  of  the 
prism  to  be  so  ordered  is  usually  divided  between  the 
two  eyes.  As  10  centrads  of  exophoria  is  considered 
normal  for  this  distance  of  33  centimeters  as  just  men- 
tioned, then  the  amount  of  prism  prescribed  will  be 
practically  the  amount  shown  in  excess  of  the  normal  10 
centrads.  For  example,  a  patient  at  fifty  years  of  age 
selects  for  each  eye  plus  one  sphere  periscopic  and  has  a 
vision  of  yj  in  each  eye  with  this  correction  and  does  not 
reveal  any  insufficiency  at  six  meters,  but  with  the  near 
correction  added  (plus  2  sphere  is  added  for  near),  then 
at  33  centimeters  there  is  found  to  be  16  centrads  of 
exophoria.  After  using  these  glasses  for  a  few  days  at 
home  the  patient  returns  complaining  that  at  close 
work  the  eyes  pain,  feel  sore  to  the  touch,  and  there 
develops  occipital  headache,  smarting  of  the  lids,  and 
blurred  vision.  The  exophoria  in  this  instance  at  33 
centimeters  is  6  centrads  in  excess  of  the  normal  amount. 
Ordering  this  amount  (six  centrads)  divided  between 

1  Some  authorities  say  five. 


HETEROPHORIA    AND   HETEROTROPIA  1 19 

the  two  eyes,  the  patient  will  receive  one  of  the  following 
prescriptions : 

I£.  O.  D.  +1.00.  S.  D.  Periscopic. 
O.  S.  +1.00.  S.  D.  Periscopic. 
SIG. — For  distance. 

Also, 

]$.  O.  D.  +3.00.  S.  D.  O  3  centrads.  Base  in,  axis  180°. 
O.  S.  +3.00.  S.  D.  o  3  centrads.  Base  in,  axis  180°. 
SIG. — For  near  only. 

Or, 

R.  O.  D.  +3.00.  S.  D.  decentered  in  10  mm. 
O.  S.  +3.00.  S.  D.  decentered  in  10  mm. 
SIG. — For  near  only. 

Or, 

1$.  O.  D.  +1.00.  S.  D.  Periscopic. 
O.  S.  +1.00.  S.  D.  Periscopic. 
SIG. — For  distance. 

Cement  on  to  lower  part  of  the  above  for  near. 

]$  O.D.  +2.00.  S.  D.  O  3  centrads.  Base  in,  axis  180°. 
O.  S.  +2.00.  S.  D.  o  3  centrads.  Base  in,  axis  180°. 
SIG. — Make  bifocals. 

If  another  patient  had  two  or  three  centrads  of 
exophoria  at  6  meters  with  the  same  correction  (i.oo 
S.  D.  Periscopic  in  each  eye)  it  would  not  be  wise  to 
give  any  distance  correction,  but  allow  him  to  use  his 
relative  hyperopia  and  at  the  same  time  to  prescribe 
the  fixation  exercises  if  he  becomes  uncomfortable  hi 
the  use  of  his  eyes  at  a  distance. 

Esophoria  (Fig.  115). — As  esophoria  is  a  tendency  of 
the  visual  axes  to  deviate  inward,  it  will  be  found  that 
some  patients  with  this  form  of  insufficiency,  when  of  two 
or  three  or  four  centrads,  suffer  very  little,  as  a  rule,  when 
using  the  eyes  at  near  work;  their  chief  discomfort 


120 


PRISMS 


arises  from  using  the  eyes  for  distant  vision.  The 
"  shopping  headache,"  the  " opera  headache,"  the 
"train  headache,"  may  be  due  to  this  form  of  insuffi- 
ciency, as  well  as  in  some  cases  of  exophoria,  but  it  is  not 
so  apt  to  cause  discomfort  if  the  full  ametropic  correction 
is  worn  constantly.  In  other  words,  if  a  hyperope  with 
esophoria  does  not  wear  his  distance  correction  and 


FIG.  115. — Tendency  of  visual  axes  inward. 

accommodates  at  the  same  time  that  he  endeavors  to 
maintain  equipoise  (relative  hyperopia),  he  may  at  times 
suffer  severely.  If  the  symptoms  of  muscular  asthenopia 
persist  after  prescribing  the  full  ametropic  correction, 
then  prisms,  bases  out,  may  be  prescribed  as  hook  fronts 
to  be  worn  over  the  constant  correction  when  using  the 
eyes  for  distance.  Prism  exercises  (prisms,  base  in)  for 
esophoria  do  not  always  benefit,  and  are  occasionally  a 


HETEROPHORIA  AND   HETEROTROPIA  121 

waste  of  time;  yet  they  should  be  tried  thoroughly  if 
the  case  appears  to  demand  it. 

When  the  patient  has  several  centrads  of  esophoria  for 
distance  he  must  use  his  full  distance  correction  and  this 
usually  corrects  any  former  discomfort  in  the  use  of  his 
eyes  for  distance ;  but  he  may  continue  to  have  discom- 
fort at  any  near  work,  such  discomfort  as  ocular  pains, 
occipital  headache,  pains  running  into  the  neck  and 
sometimes  felt  in  the  shoulders.  Such  patients  do  not 
have  any  comfort  from  their  eyes  when  reading  or  writ- 
ing or  at  any  close  work  which  requires  the  eyes  to  move 
instead  of  remaining  fixed.  For  instance,  a  sewing 
woman  will  come  with  the  story  that  she  can  sew  with 
comfort  with  her  glasses  on,  but  that  she  cannot  read 
with  comfort  and  she  cannot  understand  why.  A 
stenographer  who  runs  the  typewriter  during  the  day 
suffers  from  the  symptoms  just  described,  yet  she  can  sit 
and  sew  in  the  evening  and  not  get  a  headache.  The 
trouble  lies  in  weak  abducting  power.  The  question 
of  treatment  in  such  cases  is  not  to  weaken  adduction 
but  to  strengthen  abduction.  The  writer's  method  of 
treatment,  which  he  believes  to  be  original,  is  to  practise 
abduction  or  turning  outward  of  each  eye  while  its 
fellow  is  covered.  This  is  illustrated  in  Fig.  116.  The 
patient  is  told  to  fix  his  head  in  one  position  and  not  to 
turn  if  while  practising,  as  follows:  to  cover  the  eye 
with  a  card  as  shown  in  the  illustration  and  in  such 
manner  that  the  covered  eye  cannot  see  what  the  other 
eye  is  doing;  then,  holding  the  index-finger  point  on  a 
level  with  the  eye,  the  finger  is  gradually  made  to  de- 
scribe a  quarter  circle  or  more  to  the  same  side  as  the 


122 


PRISMS 


eye  being  exercised;  the  eye  fixes  the  point  of  the  finger 
to  the  limit  of  external  rotation.  First  one  eye  and  then 
the  other  eye  is  exercised  in  this  way  for  five  or  ten  min- 
utes after  each  meal.  Marked  improvement  will  follow 
this  treatment  in  a  few  days,  and  the  writer  can  testify 
to  some  remarkable  results  by  this  very  simple  method 


FIG.  116. 


of  strengthening  abduction.  Occasionally  this  practice 
alone  will  not  suffice  and  the  patient  will  also  have  to 
use  prism  exercises  (prisms,  bases  in). 

Hyperphoria. — Having  prescribed  the  ametropic 
correction,  an  attempt  should  be  made  to  develop  the 
innervation  of  the  weak  muscles  by  prism  exercises; 
prism  base  down  before  one  eye,  and  base  up  before  the 
other  eye.  While  this  does  not  often  give  satisfactory 


HETEROPHORIA   AND   HETEROTROPIA  123 

results,  yet  it  should  be  tried  in  each  instance.  If  prism 
exercises  do  not  correct  the  difficulty,  then  prisms  which 
overcome  most  of  the  insufficiency  should  be  prescribed 
with  the  ametropic  correction  for  constant  use.  See 
Presbyopia. 

Hyperesophoria  and  Hyperexophoria. — The  hy- 
perphoria  as  previously  stated  and  directed  is  to 
be  corrected  by  the  necessary  prism  which  is  to  be 
combined  with  the  ametropic  correction  and  the  re- 
maining esophoria  or  exophoria  to  have  any  required 
treatment  as  described  under  these  headings. 

Heterotropia  ("Cross-eye,"  strabismus,  squint  or 
manifest  squint). — This  is  a  condition  of  the  eyes  in 
which  the  amount  of  turning  of  the  eye  is  so  great 
that  it  cannot  (always)  be  overcome  by  the  effort 
of  the  patient;  and,  in  fact,  inspection  often  shows  the 
manifest  condition.  Or  heterotropia  may  be  defined 
as  the  condition  in  which  the  visual  axis  of  one  eye  is 
positively  deviated  from  the  point  of  fixation.  The  eye 
which  has  the  image  of  the  object  on  its  fovea  is  spoken 
of  as  the  fixing  eye,  while  the  other  eye  is  termed  the 
squinting  or  deviating  eye.  The  squinting  eye  does 
not  always  have  normal  visual  acuity;  and,  in  fact, 
correcting  lenses  will  not  always  produce  such  a 
result. 

As  ametropia  is  the  chief  factor  in  the  cause  of  squint, 
this  cause  must  be  promptly  removed  by  the  use  of  cor- 
recting glasses. 

The  correction  of  the  ametropia  means  four  essentials : 

i.  In  young  subjects  the  eyes  must  be  put  at  rest,  and 
kept  at  rest  for  two,  three,  or  four  weeks,  with  a  reliable 


124  PRISMS 

cycloplegic  and  dark  glasses.  Preference  is  given  to 
atropin  in  each  instance,  the  writer  considering  it  folly 
to  use  homatropin  in  such  cases. 

2.  During  the  use  of  the  cycloplegic,  the  lenses  which 
correct  the  ametropia  are  selected  with  care  and  the 
greatest  precision,  by  every  known  means  to  this  end; 
and  just  here  is  the  place  of  all  places  to  use  the  retino- 
scope,  as  most  cases  of  strabismus  appear  in  children, 
and,  too,  the  squinting  eye  often  being  amblyopic,  can- 
not assist  in  the  selection  of  the  glass. 

3.  The  correcting  glasses  are  ordered  in  the  form  of 
spectacles,  and  are  to  be  worn  from  the  time  of  rising 
until  going  to  bed.     The  strength  of  the  glasses  should 
be  as  near  the  full  correction  as  it  is  possible  to  give. 

4.  The  "drops"  are  continued  for  a  day  or  two  after 
the  glasses  have  been  obtained,  and  in  this  way,  while 
the  drops  are  still  in  the  eyes,  and  as  their  effect  slowly 
wears  away,  the  eyes  gradually  become  accustomed  to 
the  new  or  natural  order  of  accommodation  and  con- 
vergence.    After   the   cycloplegic   has   entirely   disap- 
peared, the  patient  should  be  carefully  restricted  in  the 
use   of   the   eyes  for   near-work  for  several  days   or 
weeks. 

As  hyperopia  and  astigmatism  in  combination  are 
generally  congenital  conditions,  it  therefore  follows  that 
convergent  squint  appears  quite  early  in  life,  as  soon  as 
the  child  begins  to  concentrate  its  vision  on  near  objects. 
The  squint,  at  first  periodic  or  intermittent,  finally 
becomes  constant.  Such  eyes  should  be  refracted  at 
once,  and  before  amblyopia  exanopsiacan  be  established, 
prisms  should  not  be  ordered.  It  is  interesting  to  note 


HETEROPHORIA    AND   HETEROTROPIA  125 

that  the  eyes  in  many  young  children  begin  to  fix  or  lose 
their  squint  as  soon  as  cycloplegia  is  established.  The 
prognosis  is  favorable  for  good  vision  with  glasses 
when  this  occurs.  It  will  also  be  observed  in  other 
subjects  that  while  the  drops  are  in  the  eyes  and  glasses 
worn  constantly,  the  squint  disappears  entirely;  but  as 
soon  as  the  cycloplegia  passes  away  and  near  vision  is 
attempted,  the  squint  returns,  and  vision  falls  back  in 
the  squinting  eye  to  almost  the  same  point  that  it  had 
before  the  cycloplegia.  This  occurs  in  cases  in  which  the 
amblyopia  is  becoming  established,  or  when  there  is  a 
strong  muscle  deviating  the  eye.  If  the  squint  is  due  to 


FIG.  117. 

amblyopia  exanopsia,  then  the  vision  may  be  improved 
in  one  of  two  ways.  One  way  is  to  use  drops  in  the 
fixing  eye,  and  thus  compel  the  squinting  eye  to  do  the 
seeing;  or  the  other  way  is  to  cover  the  fixing  eye  with  a 
blank  over  the  glass  (see  Fig.  117),  and  have  the  patient 
practise  in  this  way  for  one  or  two  hours  each  day,  using 
the  squinting  eye  alone. 

Worth's  Amblyoscope  or  "Fusion  Tubes." — To 
cultivate  or  develop  binocular  vision  Worth  has  given 
us  an  instrument  which  he  calls  an  amblyoscope.  (See 
Fig.  1 1 8.)  This  instrument  consists  of  two  halves 
joined  by  a  hinge.  Each  half  consists  of  a  short  tube 


126  PRISMS 

joined  to  a  longer. one  at  an  angle  of  120°;  at  the 
junction  of  the  tubes  is  an  oval  mirror.  A  translucent 
glass  object  slide  is  placed  at  the  distal  end  of  each  tube. 
At  the  hinged  ends  are  lenses  whose  focal  length  equals 
the  distance  of  the  reflected  image  of  the  object  slide; 
in  front  of  these  lenses  are  grooves  into  which  additional 
lenses  of  the  trial  case  may  be  placed  to  correct  the 
refractive  error  of  the  patient.  The  two  halves  of  the 
instrument  are  united  by  an  arc,  having  a  long  slot  at 
one  end  and  an  adjusting  screw  at  the  other.  The  object 
slides  can  be  brought  together  to  suit  a  convergence  of 


FIG.  118. — Worth's  Amblyoscope.     (Reduced  size.) 

60°,  or  a  divergence  of  the  visual  axes  of  30°.  When 
the  adjusting  screw  is  used  an  additional  movement  of 
10°  is  obtained. 

At  the  far  end  of  each  tube  there  is  also  a  square  slot 
into  each  of  which  may  be  placed  half  a  pictured  object; 
for  instance,  a  picture  of  the  right  side  of  a  man,  showing 
his  arm  and  leg  extended,  may  be  placed  in  the  left  tube, 
and  in  the  right  tube  is  placed  a  picture  of  the  same  size, 
of  the  left  side  of  the  man  with  his  leg  and  arm  similarly 
extended.  When  the  patient  looks  into  the  tubes,  the 


HETEROPHORIA   AND    HETEROTROPIA  127 

surgeon  (or  the  patient)  may  adjust  the  tubes  until  the 
two  half  pictures  unite  and  form  one  complete  picture. 
Or  the  picture  in  one  tube  may  be  a  picture  frame,  and 
in  the  other  tube  is  a  picture  of  an  animal  or  an  object, 
the  idea  being  to  have  the  patient  so  fuse  the  two  pictures 
that  the  object  is  placed  in  the  frame.  There  are  many 
different  pictures  accompanying  the  instrument  so  as 
to  give  variety  to  the  daily  exercises  and  thus  maintain 
the  patient's  interest.  This  instrument  is  certainly  a 
valuable  one  and  in  many  instances  (in  patients  under 
seven  years  of  age)  accomplishes  its  purpose. 

Cases  that  are  cured  by  correcting  the  ametropia 
must  wear  their  glasses  constantly.  Glasses  in  such 
cases  can  seldom  be  abandoned.  In  young  children  the 
squint  returns  almost  at  the  instant  the  glasses  are 
removed.  The  earliest  age  at  which  glasses  can  be 
prescribed  is  three  years  or  thereabouts,  as  it  would 
be  unreasonable  in  most  cases  to  expect  a  child  to 
appreciate  the  glasses  as  anything  but  a  toy  before 
this  age. 

The  younger  the  patient  when  glasses  are  prescribed, 
the  more  favorable  the  prognosis  and  less  likelihood  of 
a  tenotomy.  The  older  the  patient  when  glasses  are 
ordered,  the  less  the  likelihood  that  glasses  will  cure  the 
squint  and  the  greater  probability  of  a  tenotomy  being 
necessary.  This  is  explained  from  the  fact  that  the 
squint  having  persisted  for  a  long  time,  the  muscle 
which  held  the  eye  in  the  deviated  position  has  grown 
strong  and  the  opposing  muscle  weak. 

The  correction  of  squint  by  glasses  applies  particu- 
larly to  cases  of  the  concomitant  (convergent  or  diver- 


128  PRISMS 

gent)  form.  Vertical  squint  is  seldom  cured  by  cor- 
recting glasses  alone.  Prisms  should  not  be  prescribed 
for  the  correction  of  heterotropia. 

Monocular  and  alternating  squint  are  greatly  relieved 
by  the  correction  of  the  ametropia,  and  may  or  may  not 
be  cured  with  glasses  alone. 

Periodic  or  intermittent  squint,  if  due  to  permanent 
opacities  in  the  media,  cannot,  as  a  rule,  be  cured  by 
any  form  of  treatment,  but  may  be  benefited  by  the 
prescribing  of  a  prism  to  be  referred  to  later. 

It  may  be  stated  as  a  good  rule  to  follow  that  no  case 
of  squint  should  ever  be  operated  upon  until  the  glasses 
which  correct  the  ametropia  have  been  worn  constantly  for 
several  weeks  after  all  apparent  improvement  has  ceased. 
If  cases  for  operation  can  be  selected,  the  best  age  is 
about  puberty,  when  the  muscles  have  reached  a  fair 
state  of  development.  If  the  squint  is  due  to  an  ana- 
tomically short  muscle,  then  there  need  not  be  any 
great  delay  in  operating  after  glasses  have  been  ordered. 

Whenever  a  tenotomy  has  been  performed,  the  eyes 
should  again  be  carefully  refracted,  as  it  is  a  well- 
established  fact  that  tenotomy  often  relieves  a  tension 
that  will  materially  change  the  radius  of  corneal  curva- 
ture ;  and  hence  the  amount  of  the  astigmatism  and  the 
cylinder  axis  will  be  altered. 

Final  Summary. — From  the  descriptions  just  de- 
tailed it  will  be  observed  that  prisms  are  seldom  pre- 
scribed and  the  careful  refractionist  will  not  order 
prisms  with  freedom  or  impunity.  There  are  five  con- 
ditions, however,  which  warrant  the  prescribing  of 
prisms  as  follows: 


HETEROPHORIA   AND   HETEROTROPIA  I2Q 

Hyperphoria. — As  previously  stated,  the  patient  with 
hyperphoria  will  usually  accept  and  wear  a  prism  which 
corrects  about  three-fourths  of  the  amount  of  the  hyper- 
phoria, and  this  amount  may  be  divided  between  the 
two  eyes  depending,  of  course,  upon  the  strength  of  the 
prism  and  also  upon  the  strength  of  the  correcting  lenses. 
If  the  amount  is  one  or  two  centrads  which  is  to  be  pre- 
scribed, this  may  all  be  placed  before  one  eye  if  the 
lens  for  the  other  eye  is  a  strong  or  compound  one,  for 
instance,  if  the  prescription  is  as  follows: 

O.  D.  +2.ooO  +  i.oo  cyl.  axis  60° 
O.  S.   +1.00 

and  the  prism  is  a  2  base  down  before  the  right  eye,  it 
would  be  well  to  place  the  prism  base  up  before  the  left 
eye  making  it  +  i.ooO2vbase  up  axis  90°  and  in  this 
way  equalize  somewhat  the  weight  and  thickness  of  the 
lenses  for  the  two  eyes.  In  this  instance  it  would  have 
made  a  very  expensive,  cumbersome  and  heavy  lens 
for  the  right  eye,  if  the  prism  had  been  added  to  it, 
namely, 

O.  D.  +  2.ooO  +  i.oo  cyl.  axis  6oO2A.     Base  down 
axis  90°. 

In  other  words  the  prescriber  must  use  some  judgment 
in  the  matter  as  to  which  eye  is  to  receive  the  prism 
or  whether  to  put  the  entire  prism  before  one  eye  or 
divide  it  between  the  two. 

Ordering  a  Prism  after  a  Tenotomy. — When  a 
tenotomy  has  been  performed  for  the  relief  of  an  insuf- 
ciency  or  manifest  squint,  and  there  still  remains  an 

9 


130  PRISMS 

annoying  imbalance,  a  prism  that  assists  the  weak 
innervation  may  be  prescribed  for  constant  use  made 
up  in  the  lens  which  corrects  the  refractive  error.  For 
instance,  if  the  tendon  of  the  left  internal  rectus  has  been 
divided  on  account  of  a  squint  and  after  the  tenotomy 
there  remains  possibly  3,  4  or  5  centrads  of  esophoria; 
the  patient  may  have  a  3,  4  or  5  centrad  prism  ordered 
with  the  ametropic  correction,  the  base  of  the  prism  to 
be  placed  base  out  axis  180°  over  the  left  external  rectus. 
It  might  be  well  to  remember  when  prescribing  prisms 
after  a  tenotomy  that  the  base  of  the  prism  is  to  be 
placed  over  the  weak  muscle. 

Ordering  Prisms  in  Presbyopia. — This  has  already 
been  explained  in  great  part  on  page  119.  However,  the 
prescriber  should  be  on  his  guard  and  never  prescribe 
too  strong  a  prism  in  the  reading  or  near  glasses,  a  prism 
in  other  words  that  would  produce  annoying  metam- 
orphopsia.  The  way  to  guard  against  this  is  to  place 
the  prisms  (bases  in)  over  the  near  correction  and  let 
the  patient  read  the  paper  or  look  at  a  plane  or  flat  sur- 
face, such  as  the  top  of  a  table  or  a  desk  and  note  whether 
the  paper  or  table  or  desk  appears  conspicuously  con- 
vex, i.e.,  raised  in  the  middle.  If  slightly  so,  then  the  ap- 
pearance of  convexity  will  gradually  disappear  after 
wearing  the  glasses,  but  if  this  condition  is  extreme,  then 
the  strength  of  the  prisms  must  be  reduced.  Prisms, 
bases  in,  at  close  work  may  produce  the  convex  effect 
just  described  and  prisms,  bases  out,  for  esophoria  may 
produce  the  opposite  or  concave  effect. 

Prisms  for  Cosmetic  Purposes. — When  an  eye 
squints  or  is  turned  by  reason  of  injury  or  disease 


HETEROPHORIA   AND   HETEROTROPIA  131 

(corneal  opacities),  or  very  poor  vision  or  a  palsy,  and 
is  not  a  suitable  one  for  surgical  intervention,  the  wear- 
ing of  a  prism  over  such  an  eye  may  give  it  a  more 
sightly  appearance,  thus  making  it  appear  nearer  the 
normal  position  than  it  actually  is. 

Prisms  for  Cyclophoria. — Cyclophoria  is  not  a  com- 
mon condition.  It  is  the  least  common  of  the  hetero- 
phorias  and  yet  it  does  exist  and  when  present  it  should 
be  prescribed  for  in  full  with  a  correcting  prism,  using 
either  one  of  the  three  tests  for  Cyclophoria  already 
described  in  Chapter  VII. 

It  is  hoped  that  the  reader  will  not  confuse  hyper- 
esophoria  and  hyperexophoria  with  cyclophoria.  The 
descriptions  under  these  headings  should  guard  him 
against  any  such  error  in  diagnosis. 

A  prism  at  an  oblique  axis  while  it  may  temporarily 
neutralize  an  hyperesophoria  or  hyperexophoria  does 
not  necessarily  signify  that  cyclophoria  exists.  Hyper- 
esophoria and  hyperexophoria  are  to  receive  the  neces- 
sary prism  for  the  hyperphoria  only,  i.e.,  prism  base 
up  or  down,  axis  90.  (See  Hyperesophoria.)  The 
writer  does  not  advocate  prisms  at  oblique  axes  except 
in  cyclophoria  and  cyclotropia. 

When  the  diagnosis  is  made  then  the  amount  of  the 
cyclophoria  is  estimated  by  the  strength  of  the  prism 
which  is  necessary  to  make  the  lines  parallel  as  shown 
in  Fig.  104.  The  base  of  this  prism  may  be  up  or  down 
and  at  an  "off  axis,"  and  before  the  eye  which  has  the 
cyclophoria.  The  prism  is  to  be  combined  with  the 
prescription  glasses  for  constant  use. 

Cyclotropia  is  to  be  prescribed  for  in  the  same  way 


132  PRISMS 

as  cyclophoria.  Cyclotropia  is  a  very  rare  condition. 
The  writer  never  saw  but  one  such  patient  and  he  re- 
quired the  following: 

O.   D. +2. 750+0.50  cyl.   axis   15° 

O.   S.+2.75O  2A.    Base  down  axis   30°. 

These  glasses  the  patient  is  wearing  with  great  comfort 
and  satisfaction: 

Summary : — Cases  of  hyperopia  with  2  or  3  centrads 
of  esophoria  for  distance  and  near  vision  are  usually 
made  comfortable  for  all  purposes  with  a  full  correction 
of  the  refractive  error.  By  'full  correction'  is  meant 
the  cycloplegic  correction  less  0.25  sphere. 

Cases  of  hyperopia  with  orthophoria  for  infinity  and 
possibly  2  or  3  centrads  of  exophoria  for  near  should 
receive  0.50  or  0.75  less  than  the  full  cycloplegic  cor- 
rection to  be  worn  constantly. 

Cases  of  hyperopia  with  exophoria  of  3  or  4  centrads 
for  distance  should  receive  a  partial  correction  of  the 
hyperopia  and  be  instructed  in  convergent  exercises. 
When  the  exophoria  disappears  and  orthophoria  or 
esophoria  is  present  the  hyperopia  should  receive  further 
correction.  The  writer's  experience  while  it  may  differ 
from  others,  docs  not  warrant  him  in  advising  a  prism 
in  these  cases. 

Cases  of  myopia  with  exophoria  should  receive  the 
full  static  correction  if  the  eyes  are  apparently  free 
from  fundus  changes. 

Cases  of  myopia  with  esophoria  should  receive  an 
under  correction,  or  be  prescribed  for  as  if  they  were 


HETEROPHORIA  AND   HETEROTROPIA  133 

presbyopes,  i.e.,  one  correction  for  distance  and  another 
for  near. 

Hyperphoria  associated  with  any  of  the  above  men- 
tioned cases  should  receive  the  necessary  prismatic  cor- 
rection, see  page  129. 


CHAPTER  IX 

GENERAL  REMARKS  ON  PRISMS  AND  THE 
PRISMATIC  EFFECT  OF  LENSES 

That  muscle  over  which  the  base  of  a  prism  is  placed 
is  put  at  rest  to  the  extent  of  the  power  of  the  prism  so 
used ;  or  the  prism  may  be  said  to  act  as  a  sedative  to  the 
muscle  over  which  its  base  is  situated.  That  muscle 
over  which  the  edge  of  a  prism  is  placed  is  put  into 
action  to  the  extent  of  the  power  of  the  prism  so  used, 
the  prism  may  be  said  to  act  as  a  stimulant  to  the 
muscle  over  which  its  edge  is  situated. 

Prisms  with  their  bases  in  or  bases  out  could  be  worn 
if  the  eyes  would  remain  fixed,  but  on  account  of 
accommodation  and  convergence  prisms  for  the  relief 
of  esophoria  and  exophoria  in  young  patients  cannot  be 
tolerated.  A  prism  with  its  base  up  or  down  for  the  cor- 
rection of  hyperphoria  is  tolerated  and  accepted  because 
in  these  positions  the  accommodation  and  convergence 
do  not  alter  the  prism  effect  in  the  vertical  meridian. 

There  are  several  reasons  why  prisms  bases  in  or  out 
stronger  than  a  unit  cannot  be  worn  constantly  and  with 
comfort,  but  the  chief  reason  is  the  resulting  metamor- 
phopsia  or  distortion  which  appears  when  the  patient's 
eyes  are  turned  laterally  from  the  center  of  the  lenses. 

Illustrations  which  give  some  idea  of  distortion  may 
be  seen  in  Figs.  39,  40,  41  and  42. 

Another  reason  why  prisms  which  correct  esophoria 

134 


GENERAL    REMARKS    ON    PRISMS  135 

and  exophoria  cannot  be  worn  constantly,  is  that  by 
stimulation  they  soon  increase  the  amount  of  the 
esophoria  or  exophoria  and  it  is  therefore  very  bad 
treatment  to  prescribe  prisms  in  these  cases,  except  in 
the  instances  mentioned  in  the  text. 

It  seems  hardly  necessary  to  explain  to  the  reader  that 
(i)  a  convex  sphere  is  equivalent  to  prisms  with  their 
bases  at  the  center  of  the  sphere;  (2)  that  a  concave 
sphere  is  equivalent  to  prisms  with  their  edges  at  the 
center  of  the  sphere ;  (3)  that  a  convex  cylinder  is  equiva- 
lent to  prisms  with  their  bases  at  the  axis  of  the  cylinder 
and  (4)  a  concave  cylinder  is  equivalent  to  prisms  with 
their  edges  at  the  axis  of  the  cylinder;  i.e.,  (a)  on  the 
axis  of  a  cylinder  there  is  no  prismatic  effect  and  (b)  at 
the  true  center  of  a  sphere  there  is  no  prismatic  effect. 

Strong  convex  spheres  worn  before  both  eyes,  by  an 
adult  for  the  first  time  (as  he  looks  through  the  true  cen- 
ters of  these  lenses),  produce  the  effect  of  making  a  flat 
surface  appear  convex  or  raised  in  the  middle  and  as  the 
eyes  look  downward  through  the  lenses  (below  the  true 
centers)  at  the  floor,  it  appears  as  if  it  were  further  away 
than  it  actually  is  or  further  away  than  it  did  without  the 
lenses;  giving  the  patient  the  sensation  of  having  sud- 
denly grown  taller,  i.e.,  the  sense  of  "distance"  with 
these  lenses,  has  been  more  or  less  disturbed.  If  the 
convex  spheres  are  each  +  3  and  the  patient  glances 
through  them  10  millimeters  below  the  centers,  he  has 
the  effect  of  seeing  through  a  pair  of  3  prisms  bases 
upward.  If  he  looks  through  these  same  lenses  10 
millimeters  above  the  centers  an  object  appears  shorter 
than  it  actually  is,  or  if  the  patient  tips  his  head  far 


136  PRISMS 

enough  over  and  looks  through  the  lenses  above  the 
centers  at  the  floor,  the  floor  seems  closer  than  it  is 
normally  and  the  patient  has  the  sensation  of  having 
grown  shorter  in  stature. 

Such  complaints  are  not  uncommon  and  are  due 
entirely  to  the  prismatic  effect  of  the  lenses. 

Strong  concave  spheres  worn  before  both  eyes,  by 
an  adult  for  the  first  time,  produce  the  opposite  effect 
to  that  of  convex  spheres.  The  pavement  or  flat  surface 
appears  "dished"  or  hollowed  out.  If  the  spheres  are 
—3  and  the  patient  looks  downward  through  them  10 
millimeters  from  the  centers,  he  has  the  equivalent  of 
seeing  through  a  pair  of  3  prisms  bases  down;  the  floor 
or  pavement  appears  raised  or  closer  than  without  the 
lenses,  the  patient  feels  as  if  he  had  suddenly  grown 
shorter  and  the  sense  of  distance  is  correspondingly  dis- 
turbed. If  he  looks  through  these  lenses  10  millimeters 
above  the  centers,  he  has  the  sensation  of  feeling  taller, 
for  now  the  prismatic  effect  is  equivalent  to  prisms  bases 
up  and  distant  objects  appear  elongated  vertically 
(Figs.  39  and  40). 

These  optic  illusions  are  also  conspicuous  with  some 
patients  as  they  turn  their  eyes  from  right  to  left  or 
left  to  right.  Some  patients  cannot  explain  exactly 
what  the  sensation  may  be  except  to  say  that  they  feel 
more  comfortable  without  glasses  and  would  rather 
endure  poor  vision  than  wear  them.  It  is  not  always  a 
case  of  "vanity." 

Prismatic  effect  is  more  evident  with  certain  varieties 
of  spheres.  Some  patients  cannot  wear  toric  lenses  (or 
menisci)  for  this  very  reason,  they  cannot  get  accustomed 


GENERAL   REMARKS   OX  PRISMS  137 

to  toric  lenses  but  still  they  can  wear  plano-convex 
lenses.  The  writer  has  seen  patients  who  could  not 
even  wear  periscopic  lenses  on  account  of  the  distortion, 
and  wonder  how  others  wear  them  and  they  cannot. 

Nearly  all  of  these  patients  will  admit  that  they  can 
wear  their  spheres  with  pleasure  and  comfort,  it  they 
do  not  walk  around  with  them  on  or  turn  their  eyes 
from  side  to  side  and  look  through  the  edges  of  their 
lenses.  In  other  words  these  patients  have  no  trouble 
as  long  as  they  keep  their  visual  axes  on  the  line  of  the 
true  centers  of  their  lenses,  but  when  they  turn  the  visual 
axes  from  the  true  centers,  then  discomfort  comes  on 
and  persists  until  the  glasses  are  removed.  Of  course, 
and  fortunately  all  patients  are  not  alike  in  this  re- 
spect, in  fact,  it  is  the  very  few  who  are  thus  disturbed. 
Finally  some  of  the  prismatic  effect  may  be  the  result 
of  poorly  fitting  lenses,  and  naturally  this  fact  must 
have  first  consideration.  However,  it  must  be  ad- 
mitted, that  there  are  different  nervous  sensibilities  in 
different  patients.  Any  observer  along  these  lines  has 
many  opportunities  of  seeing  individuals  wearing  strong 
lenses  that  are  so  out  of  adjustment  that  one  would 
imagine  the  resulting  metamorphopsia  would  be  suffi- 
cient to  produce  migraine,  but  the  truth  is,  very  likely 
the  individual  is  only  seeing  with  one  eye  at  a  time  or 
possibly  has  "nerves  of  steel." 

A  Strong  Convex  or  Concave  Sphere  before  One 
Eye  and  a  Weak  Lens  of  Any  Variety  before  the 
Other  Eye. — Adults  whose  eyes  require  such  lenses 
also  occasionally  suffer  from  metamorphopsia  before 
they  get  accustomed  to  their  glasses,  but  the  distortion 


138  PRISMS 

complained  of  is  more  of  the  tilting  variety,  that  is  to 
say,  in  looking  at  a  plane  surface,  one  side  seems  to  slope 
upward  or  downward.  The  pavement  or  floor  seems 
raised  or  lowered  to  the  right  or  left  as  the  case  may 
be.  Yet  again  the  wearers  of  such  lenses  usually  have 
comfort  as  long  as  they  do  not  turn  their  visual  axes 
from  the  true  centers  of  the  lenses. 

A  Strong  Convex  or  Concave  Cylinder  before 
One  Eye  and  a  Weak  Lens  of  Any  Variety  before 
the  Other  Eye. — Such  a  pair  of  lenses  may  with  some 
adults  produce  metamorphopsia  similar  to  that  experi- 
enced by  patients  who  require  a  strong  sphere  before 
one  eye,  but  if  the  cylinder  axis  is  oblique,  then  these 
patients  have  a  metamorphopsia  similar  to  the  picture 
shown  in  Figs.  41  or  42.  These  patients  do  not  see 
picture  frames  as  square-cornered  but  rather  of  the 
appearance  of  a  rhombus. 

Remarks. — Young  patients  (children)  if  required  to 
wear  correcting  glasses  such  as  first  mentioned,  seldom 
refer  to  any  distortion  but  seem  to  adapt  their  vision  to 
the  glasses  without  difficulty. 

Many  patients  who  suffer  from  metamorphopsia  also 
temporarily  may  have  muscular  imbalance,  esophoria, 
exophoria  or  cyclophoria,  etc.,  that  they  never  knew  or 
complained  of  before  getting  glasses,  and  possibly  the 
metamorphopsia  is  due  as  much  to  the  temporary 
cyclophoria  as  to  the  prismatic  effect  of  the  lenses; 
however,  it  is  for  the  patient  to  persevere  and  wear  the 
lenses  and  train  his  innervation,  otherwise  there  must  be 
a  compromise  in  his  lenses  by  reducing  their  strength  and 
from  time  to  time  give  stronger  lenses  up  to  the  strength 


GENERAL    REMARKS    ON    PRISMS  139 

of  the  necessary  lens  to  correct  the  ametropia.  Prisms 
are  not  to  be  prescribed  for  such  cases  of  cyclophoria 
or  temporary  hyperphoria. 

With  all  these  cases  of  anisometropia  and  hetero- 
metropia,  the  wise  prescriber  will  have  such  patients 
test  their  vision  by  looking  at  picture  frames,  the  door, 
the  floor,  etc.,  in  his  office  before  ordering  the  glasses 
and  in  this  way  make  sure  just  how  much  distortion  does 
exist  and  let  the  patient  know  what  to  expect. 

Prismatic  Effect  in  Bifocal  Segments. — At  the  true 
center  of  a  lens  there  is  no  prismatic  effect,  but  from 
this  center  to  the  edge  of  the  lens,  the  prismatic  effect 
gradually  increases  and  the  stronger  the  lens,  the 
greater  this  prismatic  effect,  no  matter  whether  the  lens 
is  convex  or  concave.  With  this  understanding  the 
prescriber  must  bear  in  mind  when  he  orders  segments 
(scales  or  wafers),  placed  on  the  distant  correction  to 
make  bifocals,  that  it  is  the  duty  of  the  optician  to 
place  enough  prism  in  each  segment  to  counteract 
sufficiently  the  prismatic  effect  at  the  edge  of  the  lens 
used  for  distant  vision  so  as  to  give  the  segment  a 
mid-center  of  its  own. 

If  the  strength  of  both  distance  lenses  is  the  same 
then  the  prism  in  each  segment  must  be  the  same,  but 
if  the  strength  of  the  distance  lenses  is  not  the  same, 
then  the  strength  of  the  prism  in  each  segment  must  be 
different. 

The  prescriber  must  be  on  his  guard  for  this  con- 
dition of  things  and  the  prismatic  element  at  the  edge  in 
the  distance  glasses  must  be  eliminated  in  part  by  each 
segment  separately. 


140  PRISMS 

The  reader  can  readily  understand  for  himself  that 
if  the  patient's  distance  glass  was  —9.00  sphere  in  the 
right  eye,  and  —6.00  sphere  in  the  left  eye,  and  +3 
segments  are  to  be  added,  the  optician  must  add  more 
prism  base  up  to  the  right  segment  than  to  the  left  seg- 
ment, otherwise  such  a  patient  would  be  getting  a  false 
hyperphoria  when  using  the  segments. 

It  is  not  uncommon  to  hear  patients  complain  that 
they  have  tried  bifocals  and  could  not  wear  them; 
possibly  the  segments  were  not  centered. 

Prismatic  combinations  in  bifocals  were  described 
under  class  2,  presbyopes,  page  119. 

In  conclusion  and  that  the  reader  may  not  become 
confused  as  to  the  effect  of  prisms,  the  writer  takes 
great  pleasure  in  quoting  his  friend  Dr.  G.  C.  Savage 
who  says  that  "when  a  prism  base  in  or  base  out  is 
placed  before  one  eye,  only  one  nerve  center  is  excited 
and  only  one  muscle  is  brought  into  a  state  of  contrac- 
tion." "When  the  base  is  placed  up  or  down,  it  must 
excite  two  centers,  one  to  elevate  or  depress  the  eye, 
the  other  to  prevent  torsion." 


INDEX 


Abduction,  79,  80 
Aberration,  prismatic,  30 

astigmatic,  30 

chromatic,  30 
Accommodation,  134 
Achromatic  prism,  9 
Adduction,  79,  80 
Air,  14,  15 

American  Medical  Association,  47 
Ametropia,  113 

Amblyoscope,  Worth's,  125,  126 
Angle,  apical  21 

critical,  12,  13 

deviation,  20,  21 

meter,  107,  108 

refracting,  3 

of  incidence,  13 

of  refraction,  3 

tangent  of,  17,  1 8 
Anisotropic  medium,  9 
Apex,  i,  2,  6,  7 
Arc,  16,  17 

of  angle,  16 

of  radian,  17 

Arrow-scale  of  Moddox,  109,  no 
Astigmatism,  prismatic,  30 
Author's  prism  scale,  48,  49 

truncated  prism,  90,  91,  92,93 
Axis  of  cylinder,  6 

of  prism,  7,  8,  9 

visual,  63,  64 

Bar  of  prisms,  4 
Base-apex  line,  67 

of  prisms,  i,  2,  3,  4,  5 
Battery  of  prisms,  4 
Bifocal  segments,  139,  140 


Center,  geometric,  61,62 

optic,  62,  63 

true,  63 

Centimeter  scale,  50 
Centrad,  41,  42 
Circle,  16,  17 

Circular  prism,  4,  5,  6,  7,  8 
Cobalt-blue  glass,  85 
Cone,  86 

Convergence,  107,  108 
Cosmetic  purposes,  130,  131 
Cret6,  58 
Crown  glass,  15 
Critical  angle,  12,  13 
Cyclophoria,  99,  100,  101,  131 
Cyclophorometer,  103,  104 
Cyclotropia,  131 
Cylinder,  68,  69,  70,  138 

Decentered  lenses,  65,  66,  67,  68, 

69,  70,  71,  72,  73,  74 
Decentering,  64,  65 

tables  for,  75,  76,  77 
Deflection,  10,  n,  19 
Degree  prisms,  40,  41 
Dennett,  Dr.,  41,  42,  44,  45,  47 
Density,  10,  n,  15 
Deviation,  10,  n,  19 

angle  of,  18,  19,  20,  40 

maximum,  19 

minimum,  20 
Diamond,  14 
Diplopia,  57 
Dispersion,  33,  34 
Displacement,  23 
Distortion,  33 
Divergence,  78 


141 


142 


INDEX 


Dot  and  line  test,  82 

Double  prism,  85,  86,  90,  91,  92,  93 

Edge,  i,  2,  s,  6,  7 
Equilibrium,  81 
Equipoise,  81 
Esophoria,  83,  119,  120,  121 

at  distance,  119,  120,  121 

at  near,  119,  120,  121 

exercises  for,  119,  120,  121 
Exercising  prisms,  115,  120 
Exophoria,  83,  84,  119,  120 

at  distance,  119,  120 

at  near,  n 

exercises  for,  115,  116 
Eyes,  107,  108 

equilibrium  test,  82 
Eyelashes,  5 
Eyelids,  5 

Faces,  i,  2 

Fixing  eye,  123 

Flint  glass,  15 

Fresnel's  lighthouse  apparatus,  28 

Fusion  tubes,  125,  126,  127,  128 

Geneva  lens  measure,  72 
Geometric  center,  61,  62 
Glass,  cobalt  blue,  85 

crown,  15,  1 6 

flint,  15,  16 

rod,  93,  94 

ruby  red,  85 
Graefe,  von,  82 
Greek  cross  of  Ziegler,  1 1 1 

Herschel,  57 
Heterophoria,  82 
Heterotropia,  82,  123,  124,  125 
Homogeneous,  i 
Hyperesophoria,  101,  123 
Hyperexophoria,  101,  123 
Hyperphoria,  84,  85,  122,  123,  129 
Hypotenuse,  26,  27 


Ice,  15 

Illusion,  23 

Images,  23 

Incident,  angle  of,  12,  113 

ray,  12 

Inclined  surfaces,  i 
Index,  absolute,  13 

of  refraction,  13,  14,  15,  16 
Inter-ocular  distance,  108 
Isoceles  triangle,  26 
Isotropic  medium,  9 

Jackson,  Dr.  Edward,  41,  60 

Light,  28 

Lighthouse,  28,  29 
Lenses,  35,  36,  37,  38,  39 

cylinder,  68,  69,  70,  138 

decentered,  65,  66,  67,  68,  69, 
70,  71,  72,  73,  74 

prismatic,  64,  65,  66,  67,   68, 
69,  70,  71,  72,  73,  74 

spheric,  98,  135,  136,  137 
Line  cross,  112 
Lines,  6,  7 

Maddox,  85,  86,  87,  88,  89 
Malingerer,  78,  79 
Maximum  deviation,  19 
Media,  anisotropic,  9 

homogeneous,  i,  9 

isotropic,  9 
Meter  angle,  107,  108 
Metamorphopsia  30,  31,  32,  33, 
Minimum  deviation,  20 
Mirror  plane,  21,  22 
Monocular  phorometer,  106 


Noyes,  Dr.,  4 
Neutralization  of  prism,  47, 

5°,  51,  52,  53 
Number  of  prism,  6,  40,  41 

Ophthalmic  Section,  47 
Ophthalmology,  i 


48,  49 


INDEX 


Optic  axis,  64 

center,  35,  36 

illusion,  23 
Orthophoria,  81 

Phorometer,  79,  101,  102 

Crete's,  58 

cyclo-,  104,  105 

Jackson's,  60 

Meister's,  103,  104 

monocular,  105,  106 

Prince's,  102,  103 

Risley's,  59 

Savage's,  104,  105,  106,  107 

Steven's,  79,  101,  102 
Position  of  prism,  7,  8 
Prentice,Charles  F. ,  41 , 43 , 44, 45, 50 

scale,  50 
Presbyopia,  130 
Prince,  Dr.,  102,  103 
Principal  section,  3 
Prism,  i,  2,  3,  4,  5,  6,  7,  8,  9 

achromatic,  9 

angle  of,  i,  2 

axis,  7,  9 

bar,  4,  5 

base  of,  i,  2 

cobalt-blue,  85 

cone,  86,  87 

circular,  4,  5,  6,  7,  8 

combined,  54,  55,  56,  57,    58, 
S9,6o 

convergence,  79 

definition  of,  i 

divergence,  78 

double,  85,  86,  90 

effect  of,  23 

exercising,  115 

face  of,  i,  2 

general  properties,  Chapter  III 

neutralization,   47,  48,  49,  50 

S1,  52,  S3 

nomenclature,  6,  40,  41 
obtuse-angled,  85,  86 


Prism,  plane,  17 

position,  7,  8 

quadrilateral,  86,  87,  89,  90 

rectangular,  3 

ruby  red,  85 

rotary,  59 

round,  4,  5,  6,  7,  8 

section  of,  3 

shape  of,  3 

side  of,  i,  2 

square,  i,  2,  4,  5 

surface  of,  i,  2 

testing,  84 

treatment,  115,  116,  117 

Thorington,  90,  91,  92,  93 
Prismatic  aberration,  30 

action,  18,19 

astigmatism,  30 

metamorphopsia,  30 

scale,  30 
Prism-diopter,  43,  44,  45 

markings,  5,  6 

measure,  41 

sedative,  134 
Prisme  mobile,  58 
Prismometric  scale,  50 
Projection  of  image,  23 

Radian,  18 
Radiants,  17 
Rays,  13,  14 

convergent,  22 

divergent,  21,  22 

parallel,  21,  22 

reflected,  10,  n,  22 

refracted,  10,  n 
Rectangular  prism,  3 
Reflection,  27 

total,  26,  27 
Refracting  angle,  3 

surface,  2,  3 
Refraction,  Chapter  II 

index  of,  13,  14,  15 

laws  of,  10,  ii 


144 


INDEX 


Refraction   through  prism,  17,  18,      Strabismus,  123,  124 


19,  20 

Refractionist,  128 
Risley,  59 
Rock  crystal,  15 
Rod  test,  93,  94,  95,  96,  97 
Rotating  prism,  50 
Rotation  of  prisms,  55 
Ruby  red  glass,  85 

Savage,  104,  105,  106,  107,  140 

Secondary  rays,  62 

Sine,  16,  17 

Spectrum,  34 

Sphere,    spherical,    98,    135,    136, 

137 

Spirit  level,  79 
Square  prism,  i,  2,  3,  4,  5 
Squint,  123,  124 
Stevens,  79,  8 1 


Sturm's  interval,  30 

Tangent,  17 

scale,  98,  99 
Tangents,  17 
Tenotomy,  129,  130 
Total  reflection,  26,  27 
Trial-frame,  5 
True  center,  63 
Truncated  prism,  90,  91,  92,  93 

Unit  prism,  41,  42,  43,  44,  45 

Vacuum,  14 

Visual  axis,  107,  108 

Von  Graefe,  82 

Worth,  125 

Ziegler,  Dr.  L.  S.,  51,  52,  in 


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